Representation of finite groups up to isomorphism. [closed]
$begingroup$
Q1) If it is mentioned something like "a group $G$ consists of $p^2$ conjugate subgroups of order $q$" (as an example), is there a possible way to represent $G$ as isomorphic to some group by using a general representation?
Usually we can write that $G$ is isomorphic to $Z_q$ or something like that when you know some details about the group $G$. But here since it says there are $p^2$ number of sub groups what I want to know is whether it will be possible to represent all of them using up to isomorphism by some general group or will I have to know the values of $p$ and $q$ and consider them case by case?
Q2) Is there a guidance book or website where I can get a clear knowledge on determining groups up to isomorphism for a given group order? A fully explanatory guide with worked examples too if possible. (Even video lessons are ok).
Please help me in this regard.
Thanks a lot in advance.
finite-groups book-recommendation online-resources
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
$endgroup$
closed as unclear what you're asking by anomaly, ancientmathematician, Brahadeesh, Alex Provost, Rebellos Dec 22 '18 at 16:06
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Q1) If it is mentioned something like "a group $G$ consists of $p^2$ conjugate subgroups of order $q$" (as an example), is there a possible way to represent $G$ as isomorphic to some group by using a general representation?
Usually we can write that $G$ is isomorphic to $Z_q$ or something like that when you know some details about the group $G$. But here since it says there are $p^2$ number of sub groups what I want to know is whether it will be possible to represent all of them using up to isomorphism by some general group or will I have to know the values of $p$ and $q$ and consider them case by case?
Q2) Is there a guidance book or website where I can get a clear knowledge on determining groups up to isomorphism for a given group order? A fully explanatory guide with worked examples too if possible. (Even video lessons are ok).
Please help me in this regard.
Thanks a lot in advance.
finite-groups book-recommendation online-resources
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
$endgroup$
closed as unclear what you're asking by anomaly, ancientmathematician, Brahadeesh, Alex Provost, Rebellos Dec 22 '18 at 16:06
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
What are you hoping to get with worked examples that you wouldn't get with other material? If there were a simple algorithm to follow for this sort of problem, there wouldn't be any point in doing it.
$endgroup$
– anomaly
Dec 22 '18 at 5:18
add a comment |
$begingroup$
Q1) If it is mentioned something like "a group $G$ consists of $p^2$ conjugate subgroups of order $q$" (as an example), is there a possible way to represent $G$ as isomorphic to some group by using a general representation?
Usually we can write that $G$ is isomorphic to $Z_q$ or something like that when you know some details about the group $G$. But here since it says there are $p^2$ number of sub groups what I want to know is whether it will be possible to represent all of them using up to isomorphism by some general group or will I have to know the values of $p$ and $q$ and consider them case by case?
Q2) Is there a guidance book or website where I can get a clear knowledge on determining groups up to isomorphism for a given group order? A fully explanatory guide with worked examples too if possible. (Even video lessons are ok).
Please help me in this regard.
Thanks a lot in advance.
finite-groups book-recommendation online-resources
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
$endgroup$
Q1) If it is mentioned something like "a group $G$ consists of $p^2$ conjugate subgroups of order $q$" (as an example), is there a possible way to represent $G$ as isomorphic to some group by using a general representation?
Usually we can write that $G$ is isomorphic to $Z_q$ or something like that when you know some details about the group $G$. But here since it says there are $p^2$ number of sub groups what I want to know is whether it will be possible to represent all of them using up to isomorphism by some general group or will I have to know the values of $p$ and $q$ and consider them case by case?
Q2) Is there a guidance book or website where I can get a clear knowledge on determining groups up to isomorphism for a given group order? A fully explanatory guide with worked examples too if possible. (Even video lessons are ok).
Please help me in this regard.
Thanks a lot in advance.
finite-groups book-recommendation online-resources
finite-groups book-recommendation online-resources
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
edited Dec 22 '18 at 5:18
anomaly
17.6k42665
17.6k42665
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
asked Aug 7 '18 at 5:56
Buddhini AngelikaBuddhini Angelika
15910
15910
closed as unclear what you're asking by anomaly, ancientmathematician, Brahadeesh, Alex Provost, Rebellos Dec 22 '18 at 16:06
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by anomaly, ancientmathematician, Brahadeesh, Alex Provost, Rebellos Dec 22 '18 at 16:06
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
What are you hoping to get with worked examples that you wouldn't get with other material? If there were a simple algorithm to follow for this sort of problem, there wouldn't be any point in doing it.
$endgroup$
– anomaly
Dec 22 '18 at 5:18
add a comment |
$begingroup$
What are you hoping to get with worked examples that you wouldn't get with other material? If there were a simple algorithm to follow for this sort of problem, there wouldn't be any point in doing it.
$endgroup$
– anomaly
Dec 22 '18 at 5:18
$begingroup$
What are you hoping to get with worked examples that you wouldn't get with other material? If there were a simple algorithm to follow for this sort of problem, there wouldn't be any point in doing it.
$endgroup$
– anomaly
Dec 22 '18 at 5:18
$begingroup$
What are you hoping to get with worked examples that you wouldn't get with other material? If there were a simple algorithm to follow for this sort of problem, there wouldn't be any point in doing it.
$endgroup$
– anomaly
Dec 22 '18 at 5:18
add a comment |
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$begingroup$
What are you hoping to get with worked examples that you wouldn't get with other material? If there were a simple algorithm to follow for this sort of problem, there wouldn't be any point in doing it.
$endgroup$
– anomaly
Dec 22 '18 at 5:18