Question

How to use GAP to check whether an element is a square element in $G$?

score 64 · Answer 1 · 2026-04-12 01:39:04

64

Views

How to use GAP to check whether an element is a square element in $G$?

Published on 12 Apr 2026 - 1:39

score 491 · Answer 2 · 2026-04-12 01:45:42

491

Views

Index of subgroups in a finite solvable group, with trivial Frattini subgroup (Exercise 3B.12 from Finite Group Theory, by M. Isaacs)

Published on 12 Apr 2026 - 1:45

score 378 · Answer 3 · 2026-03-29 20:02:27

378

Views

Normal subgroup and singleton orbits

Published on 29 Mar 2026 - 20:02

score 98 · Answer 4 · 2020-06-02 13:47:37

98

Views

A group subset whose size divides order of the subgroup generated by it

Published on 02 Jun 2020 - 13:47

score 71 · Answer 5 · 2026-04-13 07:07:34

71

Views

Uniqueness of identity element

Published on 13 Apr 2026 - 7:07

score 30 · Answer 6 · 2026-04-13 01:12:14

30

Views

Is a character $\chi$ realizable over $K\cap L$ where $\chi$ realize over $K$ and $L$?

Published on 13 Apr 2026 - 1:12

score 117 · Answer 7 · 2026-04-13 11:54:36

117

Views

Proving no matrix of given order can exist over finite field

Published on 13 Apr 2026 - 11:54

score 3.8k · Answer 8 · 2026-04-12 02:51:06

3.8k

Views

Proving that if $H$ and $K$ are subgroups of a finite group G, then $|HK|=\frac{|H||K|}{|H \cap K|}\le |G|$.

Published on 12 Apr 2026 - 2:51

score 177 · Answer 9 · 2026-03-25 22:30:49

177

Views

How to find the number of elements of order $p$.

Published on 25 Mar 2026 - 22:30

score 443 · Answer 10 · 2026-03-26 16:06:47

443

Views

Size of quotient groups

Published on 26 Mar 2026 - 16:06

score 545 · Answer 11 · 2020-06-07 16:10:06

545

Views

Let $a$ and $b$ be elements of odd order in a finite group. Show that $a^2$ and $b^2$ commute if and only if $a$ and $b$ commute.

Published on 07 Jun 2020 - 16:10

score 74 · Answer 12 · 2026-04-13 04:08:40

74

Views

(Proof verification) For each $s \in S$, show that $\sum_{t \in Gs} \frac{1}{|Gt|}=1$

Published on 13 Apr 2026 - 4:08

score 287 · Answer 13 · 2020-06-08 00:41:24

287

Views

Let $a$ be an element of a group. Show that $a$ and $a^{-1}$ have the same order

Published on 08 Jun 2020 - 0:41

score 94 · Answer 14 · 2026-04-12 11:34:57

94

Views

Distributive law for subgroups

Published on 12 Apr 2026 - 11:34

score 430 · Answer 15 · 2026-03-29 16:49:31

430

Views

Automorphism group order when all non-identity elements have equal order

Published on 29 Mar 2026 - 16:49

List Question

How to use GAP to check whether an element is a square element in $G$?

Index of subgroups in a finite solvable group, with trivial Frattini subgroup (Exercise 3B.12 from Finite Group Theory, by M. Isaacs)

Normal subgroup and singleton orbits

A group subset whose size divides order of the subgroup generated by it

Uniqueness of identity element

Is a character $\chi$ realizable over $K\cap L$ where $\chi$ realize over $K$ and $L$?

Proving no matrix of given order can exist over finite field

Proving that if $H$ and $K$ are subgroups of a finite group G, then $|HK|=\frac{|H||K|}{|H \cap K|}\le |G|$.

How to find the number of elements of order $p$.

Size of quotient groups

Let $a$ and $b$ be elements of odd order in a finite group. Show that $a^2$ and $b^2$ commute if and only if $a$ and $b$ commute.

(Proof verification) For each $s \in S$, show that $\sum_{t \in Gs} \frac{1}{|Gt|}=1$

Let $a$ be an element of a group. Show that $a$ and $a^{-1}$ have the same order

Distributive law for subgroups

Automorphism group order when all non-identity elements have equal order

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