User James

23 votes

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Associativity test for a magma

answered Feb 8, 2013 at 17:36

14 votes

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If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian

answered Sep 12, 2014 at 21:00

13 votes

Collection of surprising identities and equations.

answered Oct 23, 2014 at 20:55

13 votes

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Does every finite non-trivial complete group have even order?

answered Sep 5, 2018 at 18:09

12 votes

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Normal Groups and Quotient Groups

answered Aug 19, 2014 at 2:35

11 votes

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Reference for the subgroup structure of $\rm{PSL}_2(q)$

answered Mar 9, 2012 at 20:14

11 votes

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Calculating the Order of An Element in A Group

answered Oct 13, 2014 at 18:10

10 votes

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Uniqueness of the direct product decomposition of finite groups

answered Aug 24, 2014 at 22:57

10 votes

Cardinality of $\text{Aut}(G\times G) $

answered Aug 28, 2014 at 0:02

10 votes

Showing that if the intersection of all subgroups other than $\langle e \rangle$ is not $\langle e \rangle$, then every element is of finite order

answered Aug 6, 2014 at 16:11

10 votes

Show that number of solutions satisfying $x^5=e$ is a multiple of 4?

answered Jun 24, 2014 at 6:15

8 votes

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the center of amalgamated product of free groups

answered Jun 11, 2014 at 5:48

8 votes

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Is there a case "infinite" p-group is meaningful?

answered Jun 12, 2014 at 3:08

8 votes

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Non-finitely generated groups with $|\text{Aut}(G)| = p$

answered Jul 2, 2014 at 6:46

8 votes

What is the easiest way to generate $\mathrm{GL}(n,\mathbb Z)$?

answered Jan 11, 2012 at 22:35

8 votes

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The order of a group presentation

answered Aug 27, 2013 at 20:49

8 votes

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Is there an infinite group that has finite subgroup with finite index?

answered Dec 14, 2015 at 21:45

8 votes

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Is there a way to describe all finite groups $G$, such that $\operatorname{Aut}(G) = D_4$?

answered Sep 23, 2018 at 14:18

7 votes

Example of $2$ non-isomorphic groups that have the same quotients

answered Mar 4, 2017 at 10:11

7 votes

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Normalizer and centralizer are equivalent when $p$ is the smallest prime dividing $|G|$

answered Oct 22, 2014 at 5:06

7 votes

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If $H$ is a normal subgroup of a finite group $G$ and $|H|=p^k$ for some prime $p$. show that $H$ is contained in every sylow $p$ subgroup of $G$

answered Aug 26, 2014 at 21:20

7 votes

Understanding Lagrange's Theorem (Group Theory)

answered Mar 22, 2013 at 17:58

7 votes

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Quasicommutative semigroups.

answered Feb 6, 2013 at 6:20

7 votes

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Maximal height of subgroups in $S_n$?

answered Aug 8, 2014 at 15:31

6 votes

Klein's 4 subgroups

answered Jun 29, 2014 at 18:50

6 votes

Conjugacy classes of non-Abelian group of order $p^3$

answered Oct 12, 2011 at 16:36

6 votes

Accepted

Given a group (finite or infinite), is there a way to find all its subgroups?

answered Dec 9, 2012 at 8:01

6 votes

Example of a specific type of infinite group

answered Oct 8, 2014 at 15:33

6 votes

Algebraic Structures: Does Order Matter?

answered Oct 8, 2014 at 20:02

6 votes

Accepted

Product of two stabilizers of transitive group action is proper subset of G?

answered Sep 10, 2014 at 16:36

Stack Exchange Network

188 Answers

Associativity test for a magma

If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian

Collection of surprising identities and equations.

Does every finite non-trivial complete group have even order?

Normal Groups and Quotient Groups

Reference for the subgroup structure of $\rm{PSL}_2(q)$

Calculating the Order of An Element in A Group

Uniqueness of the direct product decomposition of finite groups

Cardinality of $\text{Aut}(G\times G) $

Showing that if the intersection of all subgroups other than $\langle e \rangle$ is not $\langle e \rangle$, then every element is of finite order

Show that number of solutions satisfying $x^5=e$ is a multiple of 4?

the center of amalgamated product of free groups

Is there a case "infinite" p-group is meaningful?

Non-finitely generated groups with $|\text{Aut}(G)| = p$

What is the easiest way to generate $\mathrm{GL}(n,\mathbb Z)$?

The order of a group presentation

Is there an infinite group that has finite subgroup with finite index?

Is there a way to describe all finite groups $G$, such that $\operatorname{Aut}(G) = D_4$?

Example of $2$ non-isomorphic groups that have the same quotients

Normalizer and centralizer are equivalent when $p$ is the smallest prime dividing $|G|$

If $H$ is a normal subgroup of a finite group $G$ and $|H|=p^k$ for some prime $p$. show that $H$ is contained in every sylow $p$ subgroup of $G$

Understanding Lagrange's Theorem (Group Theory)

Quasicommutative semigroups.

Maximal height of subgroups in $S_n$?

Klein's 4 subgroups

Conjugacy classes of non-Abelian group of order $p^3$

Given a group (finite or infinite), is there a way to find all its subgroups?

Example of a specific type of infinite group

Algebraic Structures: Does Order Matter?

Product of two stabilizers of transitive group action is proper subset of G?