Group theory book: presentations and group actions












5














I have some basic abstract algebra knowledge (the usual groups/rings/fields).



Now I would like to study, in depth, presentations of groups and group actions. (either of which I have no knowledge)




Could someone please recommend to me books for this purpose?




(I am aware that I will most likely need two different sources (or more))



I tried to search Amazon for books on group theory but I couldn't really find a good match. There is Joseph Rotman's book on group theory and while it seems to have a bit of both, according to the reviews it is full of typos and it also contains a load of other topics.










share|cite|improve this question
























  • I don't know remember how much it has about presentations, but Dummit and Foote is good for groups and group actions.
    – Kimball
    Jan 14 '15 at 8:16






  • 2




    These two topics are not very strongly related, so you should not expect to find a single source that covers both and nothing else! I completely disagree with your disparaging remarks about Rotman's book, which is one of the books on group theory that I recommend most strongly. For example, I know of no other book at that level that includes an accessible proof of the unsolvability of the word problem in finitely presented groups.
    – Derek Holt
    Jan 14 '15 at 9:09












  • What books you followed in your first course of algebra?
    – Arpit Kansal
    Jan 14 '15 at 9:18






  • 1




    The book "Groups, Graphs and Trees" by John Meier (£20.79, second hand, amazon.co.uk) is a lovely introduction to the theory of group actions. However, flicking through it, it perhaps assumes a basic knowledge of presentations (they are only briefly introduced on page 68). On the other hand, I am a big fan of Chapter 1 of the book "Combinatorial group theory" by Magnus, Karrass and Solitar (£9.99, second hand, amazon.co.uk). It is, perhaps, the ultimate in introductions to presentations. It is also one of the classic texts in geometric and combinatorial group theory.
    – user1729
    Jan 14 '15 at 9:54






  • 1




    There is also the book "Presentations of Groups" by D.L.Johnson, but I cannot recall if it talks about actions. It does talk about (co?)homology though, and it was the only place I could find anything about cyclically presented groups. (That is, about presentations of the form $langle x_0, x_1, x_2, x_3, x_4; x_{i}x_{i+1pmod5}=x_{i+2pmod5}rangle$. This one is cyclic of order $11$, but would be infinite for large values of $5$.)
    – user1729
    Jan 14 '15 at 9:58


















5














I have some basic abstract algebra knowledge (the usual groups/rings/fields).



Now I would like to study, in depth, presentations of groups and group actions. (either of which I have no knowledge)




Could someone please recommend to me books for this purpose?




(I am aware that I will most likely need two different sources (or more))



I tried to search Amazon for books on group theory but I couldn't really find a good match. There is Joseph Rotman's book on group theory and while it seems to have a bit of both, according to the reviews it is full of typos and it also contains a load of other topics.










share|cite|improve this question
























  • I don't know remember how much it has about presentations, but Dummit and Foote is good for groups and group actions.
    – Kimball
    Jan 14 '15 at 8:16






  • 2




    These two topics are not very strongly related, so you should not expect to find a single source that covers both and nothing else! I completely disagree with your disparaging remarks about Rotman's book, which is one of the books on group theory that I recommend most strongly. For example, I know of no other book at that level that includes an accessible proof of the unsolvability of the word problem in finitely presented groups.
    – Derek Holt
    Jan 14 '15 at 9:09












  • What books you followed in your first course of algebra?
    – Arpit Kansal
    Jan 14 '15 at 9:18






  • 1




    The book "Groups, Graphs and Trees" by John Meier (£20.79, second hand, amazon.co.uk) is a lovely introduction to the theory of group actions. However, flicking through it, it perhaps assumes a basic knowledge of presentations (they are only briefly introduced on page 68). On the other hand, I am a big fan of Chapter 1 of the book "Combinatorial group theory" by Magnus, Karrass and Solitar (£9.99, second hand, amazon.co.uk). It is, perhaps, the ultimate in introductions to presentations. It is also one of the classic texts in geometric and combinatorial group theory.
    – user1729
    Jan 14 '15 at 9:54






  • 1




    There is also the book "Presentations of Groups" by D.L.Johnson, but I cannot recall if it talks about actions. It does talk about (co?)homology though, and it was the only place I could find anything about cyclically presented groups. (That is, about presentations of the form $langle x_0, x_1, x_2, x_3, x_4; x_{i}x_{i+1pmod5}=x_{i+2pmod5}rangle$. This one is cyclic of order $11$, but would be infinite for large values of $5$.)
    – user1729
    Jan 14 '15 at 9:58
















5












5








5


4





I have some basic abstract algebra knowledge (the usual groups/rings/fields).



Now I would like to study, in depth, presentations of groups and group actions. (either of which I have no knowledge)




Could someone please recommend to me books for this purpose?




(I am aware that I will most likely need two different sources (or more))



I tried to search Amazon for books on group theory but I couldn't really find a good match. There is Joseph Rotman's book on group theory and while it seems to have a bit of both, according to the reviews it is full of typos and it also contains a load of other topics.










share|cite|improve this question















I have some basic abstract algebra knowledge (the usual groups/rings/fields).



Now I would like to study, in depth, presentations of groups and group actions. (either of which I have no knowledge)




Could someone please recommend to me books for this purpose?




(I am aware that I will most likely need two different sources (or more))



I tried to search Amazon for books on group theory but I couldn't really find a good match. There is Joseph Rotman's book on group theory and while it seems to have a bit of both, according to the reviews it is full of typos and it also contains a load of other topics.







group-theory book-recommendation group-actions group-presentation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 26 at 1:59









Shaun

8,507113580




8,507113580










asked Jan 14 '15 at 7:21









user174981

19919




19919












  • I don't know remember how much it has about presentations, but Dummit and Foote is good for groups and group actions.
    – Kimball
    Jan 14 '15 at 8:16






  • 2




    These two topics are not very strongly related, so you should not expect to find a single source that covers both and nothing else! I completely disagree with your disparaging remarks about Rotman's book, which is one of the books on group theory that I recommend most strongly. For example, I know of no other book at that level that includes an accessible proof of the unsolvability of the word problem in finitely presented groups.
    – Derek Holt
    Jan 14 '15 at 9:09












  • What books you followed in your first course of algebra?
    – Arpit Kansal
    Jan 14 '15 at 9:18






  • 1




    The book "Groups, Graphs and Trees" by John Meier (£20.79, second hand, amazon.co.uk) is a lovely introduction to the theory of group actions. However, flicking through it, it perhaps assumes a basic knowledge of presentations (they are only briefly introduced on page 68). On the other hand, I am a big fan of Chapter 1 of the book "Combinatorial group theory" by Magnus, Karrass and Solitar (£9.99, second hand, amazon.co.uk). It is, perhaps, the ultimate in introductions to presentations. It is also one of the classic texts in geometric and combinatorial group theory.
    – user1729
    Jan 14 '15 at 9:54






  • 1




    There is also the book "Presentations of Groups" by D.L.Johnson, but I cannot recall if it talks about actions. It does talk about (co?)homology though, and it was the only place I could find anything about cyclically presented groups. (That is, about presentations of the form $langle x_0, x_1, x_2, x_3, x_4; x_{i}x_{i+1pmod5}=x_{i+2pmod5}rangle$. This one is cyclic of order $11$, but would be infinite for large values of $5$.)
    – user1729
    Jan 14 '15 at 9:58




















  • I don't know remember how much it has about presentations, but Dummit and Foote is good for groups and group actions.
    – Kimball
    Jan 14 '15 at 8:16






  • 2




    These two topics are not very strongly related, so you should not expect to find a single source that covers both and nothing else! I completely disagree with your disparaging remarks about Rotman's book, which is one of the books on group theory that I recommend most strongly. For example, I know of no other book at that level that includes an accessible proof of the unsolvability of the word problem in finitely presented groups.
    – Derek Holt
    Jan 14 '15 at 9:09












  • What books you followed in your first course of algebra?
    – Arpit Kansal
    Jan 14 '15 at 9:18






  • 1




    The book "Groups, Graphs and Trees" by John Meier (£20.79, second hand, amazon.co.uk) is a lovely introduction to the theory of group actions. However, flicking through it, it perhaps assumes a basic knowledge of presentations (they are only briefly introduced on page 68). On the other hand, I am a big fan of Chapter 1 of the book "Combinatorial group theory" by Magnus, Karrass and Solitar (£9.99, second hand, amazon.co.uk). It is, perhaps, the ultimate in introductions to presentations. It is also one of the classic texts in geometric and combinatorial group theory.
    – user1729
    Jan 14 '15 at 9:54






  • 1




    There is also the book "Presentations of Groups" by D.L.Johnson, but I cannot recall if it talks about actions. It does talk about (co?)homology though, and it was the only place I could find anything about cyclically presented groups. (That is, about presentations of the form $langle x_0, x_1, x_2, x_3, x_4; x_{i}x_{i+1pmod5}=x_{i+2pmod5}rangle$. This one is cyclic of order $11$, but would be infinite for large values of $5$.)
    – user1729
    Jan 14 '15 at 9:58


















I don't know remember how much it has about presentations, but Dummit and Foote is good for groups and group actions.
– Kimball
Jan 14 '15 at 8:16




I don't know remember how much it has about presentations, but Dummit and Foote is good for groups and group actions.
– Kimball
Jan 14 '15 at 8:16




2




2




These two topics are not very strongly related, so you should not expect to find a single source that covers both and nothing else! I completely disagree with your disparaging remarks about Rotman's book, which is one of the books on group theory that I recommend most strongly. For example, I know of no other book at that level that includes an accessible proof of the unsolvability of the word problem in finitely presented groups.
– Derek Holt
Jan 14 '15 at 9:09






These two topics are not very strongly related, so you should not expect to find a single source that covers both and nothing else! I completely disagree with your disparaging remarks about Rotman's book, which is one of the books on group theory that I recommend most strongly. For example, I know of no other book at that level that includes an accessible proof of the unsolvability of the word problem in finitely presented groups.
– Derek Holt
Jan 14 '15 at 9:09














What books you followed in your first course of algebra?
– Arpit Kansal
Jan 14 '15 at 9:18




What books you followed in your first course of algebra?
– Arpit Kansal
Jan 14 '15 at 9:18




1




1




The book "Groups, Graphs and Trees" by John Meier (£20.79, second hand, amazon.co.uk) is a lovely introduction to the theory of group actions. However, flicking through it, it perhaps assumes a basic knowledge of presentations (they are only briefly introduced on page 68). On the other hand, I am a big fan of Chapter 1 of the book "Combinatorial group theory" by Magnus, Karrass and Solitar (£9.99, second hand, amazon.co.uk). It is, perhaps, the ultimate in introductions to presentations. It is also one of the classic texts in geometric and combinatorial group theory.
– user1729
Jan 14 '15 at 9:54




The book "Groups, Graphs and Trees" by John Meier (£20.79, second hand, amazon.co.uk) is a lovely introduction to the theory of group actions. However, flicking through it, it perhaps assumes a basic knowledge of presentations (they are only briefly introduced on page 68). On the other hand, I am a big fan of Chapter 1 of the book "Combinatorial group theory" by Magnus, Karrass and Solitar (£9.99, second hand, amazon.co.uk). It is, perhaps, the ultimate in introductions to presentations. It is also one of the classic texts in geometric and combinatorial group theory.
– user1729
Jan 14 '15 at 9:54




1




1




There is also the book "Presentations of Groups" by D.L.Johnson, but I cannot recall if it talks about actions. It does talk about (co?)homology though, and it was the only place I could find anything about cyclically presented groups. (That is, about presentations of the form $langle x_0, x_1, x_2, x_3, x_4; x_{i}x_{i+1pmod5}=x_{i+2pmod5}rangle$. This one is cyclic of order $11$, but would be infinite for large values of $5$.)
– user1729
Jan 14 '15 at 9:58






There is also the book "Presentations of Groups" by D.L.Johnson, but I cannot recall if it talks about actions. It does talk about (co?)homology though, and it was the only place I could find anything about cyclically presented groups. (That is, about presentations of the form $langle x_0, x_1, x_2, x_3, x_4; x_{i}x_{i+1pmod5}=x_{i+2pmod5}rangle$. This one is cyclic of order $11$, but would be infinite for large values of $5$.)
– user1729
Jan 14 '15 at 9:58












1 Answer
1






active

oldest

votes


















5














It seems to me that you would like to have a book which combines aspects of geometric group theory and algebraic group theory. Here I would recommend the book Introduction to Group Theory by Oleg Bogopolski.






share|cite|improve this answer





















  • Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
    – user174981
    Jan 14 '15 at 10:20










  • Well, some parts are advanced, but you still have the basic things you need on an elementary level.
    – Dietrich Burde
    Jan 14 '15 at 10:32











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1 Answer
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active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









5














It seems to me that you would like to have a book which combines aspects of geometric group theory and algebraic group theory. Here I would recommend the book Introduction to Group Theory by Oleg Bogopolski.






share|cite|improve this answer





















  • Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
    – user174981
    Jan 14 '15 at 10:20










  • Well, some parts are advanced, but you still have the basic things you need on an elementary level.
    – Dietrich Burde
    Jan 14 '15 at 10:32
















5














It seems to me that you would like to have a book which combines aspects of geometric group theory and algebraic group theory. Here I would recommend the book Introduction to Group Theory by Oleg Bogopolski.






share|cite|improve this answer





















  • Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
    – user174981
    Jan 14 '15 at 10:20










  • Well, some parts are advanced, but you still have the basic things you need on an elementary level.
    – Dietrich Burde
    Jan 14 '15 at 10:32














5












5








5






It seems to me that you would like to have a book which combines aspects of geometric group theory and algebraic group theory. Here I would recommend the book Introduction to Group Theory by Oleg Bogopolski.






share|cite|improve this answer












It seems to me that you would like to have a book which combines aspects of geometric group theory and algebraic group theory. Here I would recommend the book Introduction to Group Theory by Oleg Bogopolski.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 14 '15 at 10:09









Dietrich Burde

77.4k64386




77.4k64386












  • Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
    – user174981
    Jan 14 '15 at 10:20










  • Well, some parts are advanced, but you still have the basic things you need on an elementary level.
    – Dietrich Burde
    Jan 14 '15 at 10:32


















  • Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
    – user174981
    Jan 14 '15 at 10:20










  • Well, some parts are advanced, but you still have the basic things you need on an elementary level.
    – Dietrich Burde
    Jan 14 '15 at 10:32
















Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
– user174981
Jan 14 '15 at 10:20




Thank you. I looked at the TOC and it looks advanced. Is it really an introduction like the title suggests?
– user174981
Jan 14 '15 at 10:20












Well, some parts are advanced, but you still have the basic things you need on an elementary level.
– Dietrich Burde
Jan 14 '15 at 10:32




Well, some parts are advanced, but you still have the basic things you need on an elementary level.
– Dietrich Burde
Jan 14 '15 at 10:32


















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