Question

Find the subgroups of $\mathbb{Z}_5 \times \mathbb{Z}_{125} \times \mathbb{Z} $

score 64 · Answer 1 · 2026-04-11 05:24:24

64

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Find the subgroups of $\mathbb{Z}_5 \times \mathbb{Z}_{125} \times \mathbb{Z} $

Published on 11 Apr 2026 - 5:24

score 179 · Answer 2 · 2026-03-30 13:41:24

179

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Let $(G,\cdot)$ be a finite abelian group and $m\in\Bbb{N}$. Prove that $S=\{g\in G\mid(o(g),m)=1\}\le G$.

Published on 30 Mar 2026 - 13:41

score 1.3k · Answer 3 · 2026-04-12 12:14:08

1.3k

Views

How to efficiently find all elements in $\langle a\rangle$ for all $a$ in $\Bbb Z / 48 \Bbb Z$

Published on 12 Apr 2026 - 12:14

score 167 · Answer 4 · 2026-04-09 03:50:00

167

Views

Centralizer of factor group

Published on 09 Apr 2026 - 3:50

score 108 · Answer 5 · 2026-04-11 18:48:37

108

Views

A group of order $340$ is isomorphic to $H\rtimes K$, with $K$ being a $2$-Sylow subgroup

Published on 11 Apr 2026 - 18:48

score 247 · Answer 6 · 2026-04-12 03:13:55

247

Views

An Exercise from Representation of Finite Groups by Serre (section 10)

Published on 12 Apr 2026 - 3:13

score 345 · Answer 7 · 2026-04-11 17:32:33

345

Views

If a subgroup $H\le S_n$ acts transitively on transpositions then $H=S_n$

Published on 11 Apr 2026 - 17:32

score 66 · Answer 8 · 2026-03-26 19:01:54

66

Views

Centralizers of elements of a normal subgroup of a finite group in GAP

Published on 26 Mar 2026 - 19:01

score 136 · Answer 9 · 2020-02-17 05:21:48

136

Views

Finding number of groups that can be formed.

Published on 17 Feb 2020 - 5:21

score 1.6k · Answer 10 · 2020-02-17 06:06:37

1.6k

Views

Number of odd and even permutation.

Published on 17 Feb 2020 - 6:06

score 108 · Answer 11 · 2026-03-26 21:34:58

108

Views

Minimal counterexample to $\frac{p - 1}{p^2}$-conjecture

Published on 26 Mar 2026 - 21:34

score 65 · Answer 12 · 2026-04-07 05:36:41

65

Views

Normal Basis Theorem and Regular Representation of $S_3$

Published on 07 Apr 2026 - 5:36

score 71 · Answer 13 · 2026-04-11 08:30:12

71

Views

A problem in finite group theory

Published on 11 Apr 2026 - 8:30

score 614 · Answer 14 · 2020-02-18 11:28:10

614

Views

A finite non cyclic group, all of whose proper subgroups are cyclic, has a non trivial proper normal subgroup.

Published on 18 Feb 2020 - 11:28

score 307 · Answer 15 · 2026-03-26 11:01:29

307

Views

Let $G$ be a finite group, $H\le G$, and $N\unlhd G$. If $|H|=5$ and $|G/N|=7$, prove $H\le N$.

Published on 26 Mar 2026 - 11:01

List Question

Find the subgroups of $\mathbb{Z}_5 \times \mathbb{Z}_{125} \times \mathbb{Z} $

Let $(G,\cdot)$ be a finite abelian group and $m\in\Bbb{N}$. Prove that $S=\{g\in G\mid(o(g),m)=1\}\le G$.

How to efficiently find all elements in $\langle a\rangle$ for all $a$ in $\Bbb Z / 48 \Bbb Z$

Centralizer of factor group

A group of order $340$ is isomorphic to $H\rtimes K$, with $K$ being a $2$-Sylow subgroup

An Exercise from Representation of Finite Groups by Serre (section 10)

If a subgroup $H\le S_n$ acts transitively on transpositions then $H=S_n$

Centralizers of elements of a normal subgroup of a finite group in GAP

Finding number of groups that can be formed.

Number of odd and even permutation.

Minimal counterexample to $\frac{p - 1}{p^2}$-conjecture

Normal Basis Theorem and Regular Representation of $S_3$

A problem in finite group theory

A finite non cyclic group, all of whose proper subgroups are cyclic, has a non trivial proper normal subgroup.

Let $G$ be a finite group, $H\le G$, and $N\unlhd G$. If $|H|=5$ and $|G/N|=7$, prove $H\le N$.

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