Question

Showing that if $G$ is a solvable finite primitive group and $M$ is a core-free maximal subgroup of $G$, then $O_p(M)=1$ where $p$ divides $|Soc(G)|$

score 115 · Answer 1 · 2026-02-23 09:32:39

115

Views

Showing that if $G$ is a solvable finite primitive group and $M$ is a core-free maximal subgroup of $G$, then $O_p(M)=1$ where $p$ divides $|Soc(G)|$

Published on 23 Feb 2026 - 9:32

score 69 · Answer 2 · 2021-06-28 11:22:42

69

Views

on the non-normal subgroups of a finite groups

Published on 28 Jun 2021 - 11:22

score 160 · Answer 3 · 2021-07-27 09:21:43

160

Views

Conjugacy classes of finite group G having size at most 4 implies G is solvable.

Published on 27 Jul 2021 - 9:21

score 410 · Answer 4 · 2021-07-29 19:16:59

410

Views

What does being closed under "extension of its members" mean?

Published on 29 Jul 2021 - 19:16

score 383 · Answer 5 · 2021-08-21 02:19:27

383

Views

Group is solvable iff every quotient has a nontrivial abelian normal subgroup

Published on 21 Aug 2021 - 2:19

score 217 · Answer 6 · 2021-08-23 20:08:46

217

Views

Normalizers/centralizers of Sylow 2 subgroups of subgroups of a finite solvable group with elementary abelian sylow subgroup

Published on 23 Aug 2021 - 20:08

score 167 · Answer 7 · 2021-08-26 11:55:18

167

Views

Why Should I Care about Solvability by Radicals?

Published on 26 Aug 2021 - 11:55

score 96 · Answer 8 · 2026-03-26 06:17:40

96

Views

Solvability, nilpotence and permutation Groups

Published on 26 Mar 2026 - 6:17

score 108 · Answer 9 · 2021-09-02 06:52:17

108

Views

Any group of order $p^2q$ (p,q primes) is solvable

Published on 02 Sep 2021 - 6:52

score 436 · Answer 10 · 2021-09-03 22:12:33

436

Views

Let $G$ be a finite solvable group, all of whose Sylow subgroups are abelian. Prove that $Z(G) \cap G' = 1$.

Published on 03 Sep 2021 - 22:12

score 152 · Answer 11 · 2021-09-04 04:56:54

152

Views

Show that the Galois group of the polynomial $f(x)=x^{5}-5 x^{4}+10 x^{3}-$ $10 x^{2}+5 x-3$ is solvable

Published on 04 Sep 2021 - 4:56

score 473 · Answer 12 · 2021-09-14 12:35:12

473

Views

Show that $G$ is not solvable iff it contains a normal non trivial subgroup with $H=H'$

Published on 14 Sep 2021 - 12:35

score 65 · Answer 13 · 2021-09-14 13:32:27

65

Views

Fitting group of a soluble group

Published on 14 Sep 2021 - 13:32

score 402 · Answer 14 · 2021-09-17 01:07:16

402

Views

Abelian Subgroup of Normal Subgroup of Solvable Group

Published on 17 Sep 2021 - 1:07

score 62 · Answer 15 · 2021-09-17 14:33:46

62

Views

Solvable groups of order $mn$ with $(m,n)=1$

Published on 17 Sep 2021 - 14:33

List Question

Showing that if $G$ is a solvable finite primitive group and $M$ is a core-free maximal subgroup of $G$, then $O_p(M)=1$ where $p$ divides $|Soc(G)|$

on the non-normal subgroups of a finite groups

Conjugacy classes of finite group G having size at most 4 implies G is solvable.

What does being closed under "extension of its members" mean?

Group is solvable iff every quotient has a nontrivial abelian normal subgroup

Normalizers/centralizers of Sylow 2 subgroups of subgroups of a finite solvable group with elementary abelian sylow subgroup

Why Should I Care about Solvability by Radicals?

Solvability, nilpotence and permutation Groups

Any group of order $p^2q$ (p,q primes) is solvable

Let $G$ be a finite solvable group, all of whose Sylow subgroups are abelian. Prove that $Z(G) \cap G' = 1$.

Show that the Galois group of the polynomial $f(x)=x^{5}-5 x^{4}+10 x^{3}-$ $10 x^{2}+5 x-3$ is solvable

Show that $G$ is not solvable iff it contains a normal non trivial subgroup with $H=H'$

Fitting group of a soluble group

Abelian Subgroup of Normal Subgroup of Solvable Group

Solvable groups of order $mn$ with $(m,n)=1$

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