Question

Group of order $|G|=6545$ has either a normal Sylow 5-subgroup or a normal Sylow 17-subgroup.

score 1.9k · Answer 1 · 2026-04-16 15:23:31

1.9k

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Group of order $|G|=6545$ has either a normal Sylow 5-subgroup or a normal Sylow 17-subgroup.

Published on 16 Apr 2026 - 15:23

score 128 · Answer 2 · 2026-04-14 18:08:39

128

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Sylow subgroups/subgroup lattices in algebraic topology?

Published on 14 Apr 2026 - 18:08

score 64 · Answer 3 · 2026-04-16 13:54:05

64

Views

On the non-nilpotent solvable groups

Published on 16 Apr 2026 - 13:54

score 1.9k · Answer 4 · 2026-04-30 10:59:19

1.9k

Views

A group of order 20

Published on 30 Apr 2026 - 10:59

score 214 · Answer 5 · 2026-04-15 03:55:22

214

Views

Show that $GL_2(\mathbb{F}_p)$ has only one conjugacy class of order $p$.

Published on 15 Apr 2026 - 3:55

score 171 · Answer 6 · 2026-04-15 03:18:52

171

Views

Finite simple group $G$ containing no elements of order $5$

Published on 15 Apr 2026 - 3:18

score 97 · Answer 7 · 2026-04-11 19:19:50

97

Views

Question about proof of classifying groups of order $pq$

Published on 11 Apr 2026 - 19:19

score 78 · Answer 8 · 2026-04-10 20:50:43

78

Views

On the subgroups properties of $A_5$

Published on 10 Apr 2026 - 20:50

score 1.6k · Answer 9 · 2026-05-10 13:26:30

1.6k

Views

How to prove that a finite group of order $280$ is not simple?

Published on 10 May 2026 - 13:26

score 506 · Answer 10 · 2026-04-17 09:17:29

506

Views

How to prove: if $G$ finite, $P$ a subgroup or order $p$ and $P = C_G(P)$ then $P$ is a Sylow $p$-subgroup of $G$

Published on 17 Apr 2026 - 9:17

score 725 · Answer 11 · 2026-03-31 08:28:53

725

Views

Find the $5$-sylow subgroup of the symmetric group $S_{24}$

Published on 31 Mar 2026 - 8:28

score 1.3k · Answer 12 · 2026-05-10 13:26:09

1.3k

Views

Show that every group of order $5865$ is cyclic

Published on 10 May 2026 - 13:26

score 883 · Answer 13 · 2026-05-10 13:26:23

883

Views

Prove that there is no simple group of order $144$

Published on 10 May 2026 - 13:26

score 538 · Answer 14 · 2026-04-17 00:30:45

538

Views

Prove that any group of order 392 has a normal group of order 7 or 49

Published on 17 Apr 2026 - 0:30

score 223 · Answer 15 · 2026-04-16 05:54:52

223

Views

Let$G$ be a group of order $12$ with $4$ Sylow $3$-subgroups, affording permutation representation $\phi : G \to S_4$. Prove that $ker \phi = 1$.

Published on 16 Apr 2026 - 5:54

List Question

Group of order $|G|=6545$ has either a normal Sylow 5-subgroup or a normal Sylow 17-subgroup.

Sylow subgroups/subgroup lattices in algebraic topology?

On the non-nilpotent solvable groups

A group of order 20

Show that $GL_2(\mathbb{F}_p)$ has only one conjugacy class of order $p$.

Finite simple group $G$ containing no elements of order $5$

Question about proof of classifying groups of order $pq$

On the subgroups properties of $A_5$

How to prove that a finite group of order $280$ is not simple?

How to prove: if $G$ finite, $P$ a subgroup or order $p$ and $P = C_G(P)$ then $P$ is a Sylow $p$-subgroup of $G$

Find the $5$-sylow subgroup of the symmetric group $S_{24}$

Show that every group of order $5865$ is cyclic

Prove that there is no simple group of order $144$

Prove that any group of order 392 has a normal group of order 7 or 49

Let$G$ be a group of order $12$ with $4$ Sylow $3$-subgroups, affording permutation representation $\phi : G \to S_4$. Prove that $ker \phi = 1$.

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