Tor of a group and counter example [duplicate]
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Torsion elements of a group aren't necessarily a subgroup [duplicate]
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Let $Tor(G) = { g in G | exists n >0 , g^n = e }$ of a group $G$ , give an example to $G$ such that $Tor(G)$ is not sub group ?
Easy to prove that $G$ must be non-Abelian and infinite in size, so i thought of matrix but i don't have concrete example
group-theory
asked Nov 23 at 10:31
Ahmad
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marked as duplicate by lulu, Saucy O'Path, Christopher, amWhy group-theory
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Nov 23 at 14:40
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Torsion elements of a group aren't necessarily a subgroup [duplicate]
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Let $Tor(G) = { g in G | exists n >0 , g^n = e }$ of a group $G$ , give an example to $G$ such that $Tor(G)$ is not sub group ?
Easy to prove that $G$ must be non-Abelian and infinite in size, so i thought of matrix but i don't have concrete example
group-theory
asked Nov 23 at 10:31
Ahmad
2,4921625
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Nov 23 at 14:40
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This question already has an answer here:
Torsion elements of a group aren't necessarily a subgroup [duplicate]
1 answer
Let $Tor(G) = { g in G | exists n >0 , g^n = e }$ of a group $G$ , give an example to $G$ such that $Tor(G)$ is not sub group ?
Easy to prove that $G$ must be non-Abelian and infinite in size, so i thought of matrix but i don't have concrete example
group-theory
asked Nov 23 at 10:31
Ahmad
2,4921625
This question already has an answer here:
Torsion elements of a group aren't necessarily a subgroup [duplicate]
1 answer
Let $Tor(G) = { g in G | exists n >0 , g^n = e }$ of a group $G$ , give an example to $G$ such that $Tor(G)$ is not sub group ?
Easy to prove that $G$ must be non-Abelian and infinite in size, so i thought of matrix but i don't have concrete example
This question already has an answer here:
Torsion elements of a group aren't necessarily a subgroup [duplicate]
1 answer
group-theory
group-theory
asked Nov 23 at 10:31
Ahmad
2,4921625
asked Nov 23 at 10:31
Ahmad
2,4921625
asked Nov 23 at 10:31
Ahmad
2,4921625
asked Nov 23 at 10:31
Ahmad
2,4921625
asked Nov 23 at 10:31
Ahmad
2,4921625
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Nov 23 at 14:40
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Nov 23 at 14:40
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2 Answers
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Take $langle x,y | x^2=y^2=1rangle$.
answered Nov 23 at 10:55
freakish
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I think the above answer is better, but here's one too. Take the infinite dihedral group. It's generated by reflections (which are torsion elts).
answered Nov 23 at 10:59
Richard Martin
1,62618
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2 Answers
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2 Answers
2
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active
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active
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up vote
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Take $langle x,y | x^2=y^2=1rangle$.
answered Nov 23 at 10:55
freakish
11.1k1628
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up vote
3
down vote
Take $langle x,y | x^2=y^2=1rangle$.
answered Nov 23 at 10:55
freakish
11.1k1628
add a comment |
up vote
3
down vote
up vote
3
down vote
Take $langle x,y | x^2=y^2=1rangle$.
answered Nov 23 at 10:55
freakish
11.1k1628
Take $langle x,y | x^2=y^2=1rangle$.
answered Nov 23 at 10:55
freakish
11.1k1628
answered Nov 23 at 10:55
freakish
11.1k1628
answered Nov 23 at 10:55
freakish
11.1k1628
answered Nov 23 at 10:55
freakish
11.1k1628
11.1k1628
add a comment |
add a comment |
up vote
1
down vote
I think the above answer is better, but here's one too. Take the infinite dihedral group. It's generated by reflections (which are torsion elts).
answered Nov 23 at 10:59
Richard Martin
1,62618
add a comment |
up vote
1
down vote
I think the above answer is better, but here's one too. Take the infinite dihedral group. It's generated by reflections (which are torsion elts).
answered Nov 23 at 10:59
Richard Martin
1,62618
add a comment |
up vote
1
down vote
up vote
1
down vote
I think the above answer is better, but here's one too. Take the infinite dihedral group. It's generated by reflections (which are torsion elts).
answered Nov 23 at 10:59
Richard Martin
1,62618
I think the above answer is better, but here's one too. Take the infinite dihedral group. It's generated by reflections (which are torsion elts).
answered Nov 23 at 10:59
Richard Martin
1,62618
answered Nov 23 at 10:59
Richard Martin
1,62618
answered Nov 23 at 10:59
Richard Martin
1,62618
answered Nov 23 at 10:59
Richard Martin
1,62618
1,62618
add a comment |
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