Question

Every group of order $60$ , having a normal subgroup of order $2$ , has a normal subgroup of order $6$ (without Sylow )?

score 921 · Answer 1 · 2026-04-02 15:24:33

921

Views

Every group of order $60$ , having a normal subgroup of order $2$ , has a normal subgroup of order $6$ (without Sylow )?

Published on 02 Apr 2026 - 15:24

score 465 · Answer 2 · 2016-01-21 16:10:38

465

Views

$G$ is doubly transitive on a set $S$ if and only if $G=HTH$ where $H$ is an isotropy subgroup and $T$ is a group of order 2 not contained in $H$.

Published on 21 Jan 2016 - 16:10

score 65 · Answer 3 · 2016-01-22 10:50:28

65

Views

Smooth actions and stabilizer

Published on 22 Jan 2016 - 10:50

score 585 · Answer 4 · 2026-03-03 14:57:52

585

Views

Questions about the definition of a periodic pattern

Published on 03 Mar 2026 - 14:57

score 109 · Answer 5 · 2016-01-24 11:24:34

109

Views

Is the axiom $g1 = g$ essential for a group action

Published on 24 Jan 2016 - 11:24

score 89 · Answer 6 · 2016-01-25 21:26:44

89

Views

Properly discontinuous action of a group

Published on 25 Jan 2016 - 21:26

score 63 · Answer 7 · 2016-01-28 02:48:38

63

Views

Properties of minimal $\mathbb{Z}$-actions on infinite compact spaces

Published on 28 Jan 2016 - 2:48

score 96 · Answer 8 · 2016-01-28 18:36:45

96

Views

How does cycle index change along an equivariant map?

Published on 28 Jan 2016 - 18:36

score 384 · Answer 9 · 2016-01-28 23:16:36

384

Views

Group Action: Group $(\mathbb{Z}, +)$ acting on $\mathbb{R}$

Published on 28 Jan 2016 - 23:16

score 152 · Answer 10 · 2016-01-29 03:15:41

152

Views

Invariant complement to a $G$-module (not necessarily a vector space)

Published on 29 Jan 2016 - 3:15

score 189 · Answer 11 · 2016-01-29 18:14:22

189

Views

A description of the transporter $\operatorname{Tran}_G(H,K)$ for subgroups $H\le K$

Published on 29 Jan 2016 - 18:14

score 2.7k · Answer 12 · 2026-04-02 15:16:00

2.7k

Views

$G$ be a group of order $pn$ , where $p$ is a prime and $p>n$ , then is it true that any subgroup of order $p$ is normal in $G$?

Published on 02 Apr 2026 - 15:16

score 308 · Answer 13 · 2016-02-04 02:24:29

$H$ be a proper subgroup of finite group $G$ such that $H \cap gHg^{-1}=\{e\} , \forall g \in G \setminus H$ , then $|\cup gHg^{-1}|>\dfrac 12 |G|+1$

score 44 · Answer 14 · 2016-02-04 06:37:39

44

Views

Prove the set of permuations which permute only finitely many elements is a normal subgroup

Published on 04 Feb 2016 - 6:37

score 69 · Answer 15 · 2016-02-04 07:17:03

69

Views

Prove that if $\tau \in N_{S_A}(H)$ then $\tau$ stabilizes the sets $F(H)$ and $A \backslash F(H)$

Published on 04 Feb 2016 - 7:17

List Question

Every group of order $60$ , having a normal subgroup of order $2$ , has a normal subgroup of order $6$ (without Sylow )?

$G$ is doubly transitive on a set $S$ if and only if $G=HTH$ where $H$ is an isotropy subgroup and $T$ is a group of order 2 not contained in $H$.

Smooth actions and stabilizer

Questions about the definition of a periodic pattern

Is the axiom $g1 = g$ essential for a group action

Properly discontinuous action of a group

Properties of minimal $\mathbb{Z}$-actions on infinite compact spaces

How does cycle index change along an equivariant map?

Group Action: Group $(\mathbb{Z}, +)$ acting on $\mathbb{R}$

Invariant complement to a $G$-module (not necessarily a vector space)

A description of the transporter $\operatorname{Tran}_G(H,K)$ for subgroups $H\le K$

$G$ be a group of order $pn$ , where $p$ is a prime and $p>n$ , then is it true that any subgroup of order $p$ is normal in $G$?

$H$ be a proper subgroup of finite group $G$ such that $H \cap gHg^{-1}=\{e\} , \forall g \in G \setminus H$ , then $|\cup gHg^{-1}|>\dfrac 12 |G|+1$

Prove the set of permuations which permute only finitely many elements is a normal subgroup

Prove that if $\tau \in N_{S_A}(H)$ then $\tau$ stabilizes the sets $F(H)$ and $A \backslash F(H)$

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