Question

Prove that there is no $\{3,5\}$-Hall subgroup in $A_{5}$

score 64 · Answer 1 · 2018-09-29 02:09:15

64

Views

Prove that there is no $\{3,5\}$-Hall subgroup in $A_{5}$

Published on 29 Sep 2018 - 2:09

score 98 · Answer 2 · 2018-09-29 15:54:04

98

Views

The structure of $\Bbb Z_n=\{ kmod(p)|(n,p)=1\}$

Published on 29 Sep 2018 - 15:54

score 48 · Answer 3 · 2026-03-26 01:12:46

48

Views

Suppose that $H$ is a subgroup, of order $p$ (a prime), of a group $G$, of order $< p^2$ . Show that $H\trianglelefteq G$

Published on 26 Mar 2026 - 1:12

score 631 · Answer 4 · 2018-09-30 07:50:19

631

Views

Frattini's argument and normalizers Dummit chapter 6

Published on 30 Sep 2018 - 7:50

score 3.2k · Answer 5 · 2018-09-30 08:44:40

3.2k

Views

Every group with order prime power $p^n$ then it has subgroup of order $p^k$ for $0\leq k \leq n$

Published on 30 Sep 2018 - 8:44

score 87 · Answer 6 · 2026-03-26 09:42:47

87

Views

Does $P^g=\{gpg^{-1}|g \in G\}$ have the same order as P, where |P|=7

Published on 26 Mar 2026 - 9:42

score 109 · Answer 7 · 2018-09-30 20:41:34

109

Views

Prove that a subgroup P is normal in G, where |P|=p and $|G|<p^2$

Published on 30 Sep 2018 - 20:41

score 139 · Answer 8 · 2026-03-25 07:40:46

139

Views

Sylow $p$-Subgroups and Counting Prime Numbers

Published on 25 Mar 2026 - 7:40

score 1k · Answer 9 · 2026-03-28 06:24:07

1k

Views

How to check whether a representation $G\to\mathrm{GL}(n,\Bbb R)$ is irreducible?

Published on 28 Mar 2026 - 6:24

score 130 · Answer 10 · 2026-03-25 16:07:02

130

Views

conceptual question with example: proving groups are isomorphic

Published on 25 Mar 2026 - 16:07

score 194 · Answer 11 · 2026-03-25 17:21:34

194

Views

Cardinality of product of subsets of a group

Published on 25 Mar 2026 - 17:21

score 52 · Answer 12 · 2026-03-25 22:04:37

52

Views

Does the symmetric group $\mathfrak{S}_9$ contain a noncyclic subgroup of order 9?

Published on 25 Mar 2026 - 22:04

score 92 · Answer 13 · 2026-03-25 23:23:29

92

Views

Can I find a series where an abelian series of smallest possible length is different from derived series?

Published on 25 Mar 2026 - 23:23

score 2.8k · Answer 14 · 2026-03-26 23:11:00

2.8k

Views

A group of order $n$ is cyclic if and only if it contains an element of order $n$.

Published on 26 Mar 2026 - 23:11

score 243 · Answer 15 · 2026-03-25 23:25:39

243

Views

Write $\mathbb{Z}_{20}^{\times}$ as a product of p-power cyclic groups.

Published on 25 Mar 2026 - 23:25

List Question

Prove that there is no $\{3,5\}$-Hall subgroup in $A_{5}$

The structure of $\Bbb Z_n=\{ kmod(p)|(n,p)=1\}$

Suppose that $H$ is a subgroup, of order $p$ (a prime), of a group $G$, of order $< p^2$ . Show that $H\trianglelefteq G$

Frattini's argument and normalizers Dummit chapter 6

Every group with order prime power $p^n$ then it has subgroup of order $p^k$ for $0\leq k \leq n$

Does $P^g=\{gpg^{-1}|g \in G\}$ have the same order as P, where |P|=7

Prove that a subgroup P is normal in G, where |P|=p and $|G|<p^2$

Sylow $p$-Subgroups and Counting Prime Numbers

How to check whether a representation $G\to\mathrm{GL}(n,\Bbb R)$ is irreducible?

conceptual question with example: proving groups are isomorphic

Cardinality of product of subsets of a group

Does the symmetric group $\mathfrak{S}_9$ contain a noncyclic subgroup of order 9?

Can I find a series where an abelian series of smallest possible length is different from derived series?

A group of order $n$ is cyclic if and only if it contains an element of order $n$.

Write $\mathbb{Z}_{20}^{\times}$ as a product of p-power cyclic groups.

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