Question

Help understanding proof: classifying groups of order $21$

score 112 · Answer 1 · 2023-04-06 14:37:16

112

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Help understanding proof: classifying groups of order $21$

Published on 06 Apr 2023 - 14:37

score 50 · Answer 2 · 2023-04-08 15:01:54

50

Views

Why does $K=\Bbb F_p[\theta_n]$ contains subfield of order $p^e$ with solutions to $X^{pe}-X=0$ over $K$ where $e$ is the exponent of $p\pmod n$?

Published on 08 Apr 2023 - 15:01

score 36 · Answer 3 · 2023-04-15 04:48:55

36

Views

For odd prime $p$, $\Bbb F^\times_{p^2}\subset\mathrm{GL}_2(\Bbb F_p)$

Published on 15 Apr 2023 - 4:48

score 77 · Answer 4 · 2023-04-19 03:57:52

77

Views

To construct a group with certain properties.

Published on 19 Apr 2023 - 3:57

score 272 · Answer 5 · 2023-04-21 17:39:43

272

Views

Showing that a group of order $72$ has a normal subgroup of order at least $3$

Published on 21 Apr 2023 - 17:39

score 99 · Answer 6 · 2023-04-25 17:23:10

99

Views

How many copies of $D_4$ in $S_5$?

Published on 25 Apr 2023 - 17:23

score 118 · Answer 7 · 2023-04-25 22:00:54

118

Views

$3$-Sylows of $A_7$

Published on 25 Apr 2023 - 22:00

score 80 · Answer 8 · 2023-04-26 01:24:32

80

Views

Example Sylow Subgroup of $A_5$

Published on 26 Apr 2023 - 1:24

score 109 · Answer 9 · 2023-04-27 11:24:20

109

Views

Dummit & Foote's Abstract Algebra: Error on proof of Sylow's theorem (Theorem 4.5.18)

Published on 27 Apr 2023 - 11:24

score 82 · Answer 10 · 2023-05-02 01:46:41

82

Views

Sylow P-Subgroups of Normal Subgroups

Published on 02 May 2023 - 1:46

score 109 · Answer 11 · 2023-05-03 03:43:36

109

Views

Do normalizers of $p$-subgroups of $S_n$ always grow?

Published on 03 May 2023 - 3:43

score 34 · Answer 12 · 2026-03-29 00:00:08

34

Views

$N \cong (\mathbb{Z}/p\mathbb{Z}) \rtimes_{\varphi} (\mathbb{Z}/p\mathbb{Z})^{\times}$ where $N$ is the normalizer of Sylow $p$-subgroup of $S_p$

Published on 29 Mar 2026 - 0:00

score 139 · Answer 13 · 2026-03-27 02:34:42

139

Views

When does $|G|=pq$ admit unique non abelian representation?

Published on 27 Mar 2026 - 2:34

score 88 · Answer 14 · 2023-05-13 01:52:10

88

Views

a doubt on Sylow's Theorem in Dummit&Foote's Abstract Algebra

Published on 13 May 2023 - 1:52

score 45 · Answer 15 · 2023-05-14 23:26:19

45

Views

if $G$ is a finite nilpotent group $n$-generated, then is any Sylow subgroup at most $n$-generated?

Published on 14 May 2023 - 23:26

List Question

Help understanding proof: classifying groups of order $21$

Why does $K=\Bbb F_p[\theta_n]$ contains subfield of order $p^e$ with solutions to $X^{pe}-X=0$ over $K$ where $e$ is the exponent of $p\pmod n$?

For odd prime $p$, $\Bbb F^\times_{p^2}\subset\mathrm{GL}_2(\Bbb F_p)$

To construct a group with certain properties.

Showing that a group of order $72$ has a normal subgroup of order at least $3$

How many copies of $D_4$ in $S_5$?

$3$-Sylows of $A_7$

Example Sylow Subgroup of $A_5$

Dummit & Foote's Abstract Algebra: Error on proof of Sylow's theorem (Theorem 4.5.18)

Sylow P-Subgroups of Normal Subgroups

Do normalizers of $p$-subgroups of $S_n$ always grow?

$N \cong (\mathbb{Z}/p\mathbb{Z}) \rtimes_{\varphi} (\mathbb{Z}/p\mathbb{Z})^{\times}$ where $N$ is the normalizer of Sylow $p$-subgroup of $S_p$

When does $|G|=pq$ admit unique non abelian representation?

a doubt on Sylow's Theorem in Dummit&Foote's Abstract Algebra

if $G$ is a finite nilpotent group $n$-generated, then is any Sylow subgroup at most $n$-generated?

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