Question

Constructing homomorphisms between a group and its subgroup

score 3.1k · Answer 1 · 2026-03-29 16:01:15

3.1k

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Constructing homomorphisms between a group and its subgroup

Published on 29 Mar 2026 - 16:01

score 818 · Answer 2 · 2017-01-01 20:19:40

818

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Show that Centralizer is a subgroup of Normalizer - Intermediate Step

Published on 01 Jan 2017 - 20:19

score 1.1k · Answer 3 · 2017-01-02 05:25:59

1.1k

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$H\trianglelefteq G$, $H$ intersects the commutator subgroup of $G$ trivially implies $H$ in center of $G$?

Published on 02 Jan 2017 - 5:25

score 382 · Answer 4 · 2017-01-02 11:29:31

382

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Intersection of two cosets of two different normal subgroups of finite index is a coset of a normal subgroup of finite index

Published on 02 Jan 2017 - 11:29

score 491 · Answer 5 · 2026-03-25 17:40:23

491

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Residually finite extension of a finite group

Published on 25 Mar 2026 - 17:40

score 1.5k · Answer 6 · 2026-03-26 17:33:39

1.5k

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Direct product of two nilpotent groups is nilpotent and direct product of two solvable groups is solvable

Published on 26 Mar 2026 - 17:33

score 377 · Answer 7 · 2026-02-23 04:41:46

377

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Existence of a normal $p$-complement. (5C.12 Finite Group Theory, Isaacs)

Published on 23 Feb 2026 - 4:41

score 41 · Answer 8 · 2026-03-25 23:36:55

41

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Reducing a set into a subset that still contains every attribute found in the original set?

Published on 25 Mar 2026 - 23:36

score 60 · Answer 9 · 2026-02-23 13:46:24

60

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The exponent subgroup $n\Bbb{Z}$ inducing a nontrivial $X^n - 1 = 0$ solution subgroup of $R^{\times}$ for a ring $R$ with $1$.

Published on 23 Feb 2026 - 13:46

score 181 · Answer 10 · 2017-01-13 16:21:40

181

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Proving that $(aH)^{m} = H$ for any $a \in G$, with $H\triangleleft G$ and $(G:H)=m$

Published on 13 Jan 2017 - 16:21

score 1k · Answer 11 · 2026-03-30 11:43:18

1k

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What are the self-normalizing subgroups of $S_n$?

Published on 30 Mar 2026 - 11:43

score 5.4k · Answer 12 · 2017-01-15 11:27:19

5.4k

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If $G$ is a finite group and $H$ is a normal subgroup of $G$,then prove that $o(G/H)=o(G)/o(H).$

Published on 15 Jan 2017 - 11:27

score 100 · Answer 13 · 2026-03-30 11:35:59

100

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Find a subgroup of $S_n$, given its normalizer

Published on 30 Mar 2026 - 11:35

score 1.1k · Answer 14 · 2026-03-28 07:57:04

1.1k

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Normal Subgroups of $O(n)$

Published on 28 Mar 2026 - 7:57

score 115 · Answer 15 · 2017-01-21 09:54:46

115

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Group theory $G \triangleright H , H \cong \mathbb{Z}, G/H \cong \mathbb{Z}/ n \mathbb{Z}$.Then Classfication of $G$

Published on 21 Jan 2017 - 9:54

List Question

Constructing homomorphisms between a group and its subgroup

Show that Centralizer is a subgroup of Normalizer - Intermediate Step

$H\trianglelefteq G$, $H$ intersects the commutator subgroup of $G$ trivially implies $H$ in center of $G$?

Intersection of two cosets of two different normal subgroups of finite index is a coset of a normal subgroup of finite index

Residually finite extension of a finite group

Direct product of two nilpotent groups is nilpotent and direct product of two solvable groups is solvable

Existence of a normal $p$-complement. (5C.12 Finite Group Theory, Isaacs)

Reducing a set into a subset that still contains every attribute found in the original set?

The exponent subgroup $n\Bbb{Z}$ inducing a nontrivial $X^n - 1 = 0$ solution subgroup of $R^{\times}$ for a ring $R$ with $1$.

Proving that $(aH)^{m} = H$ for any $a \in G$, with $H\triangleleft G$ and $(G:H)=m$

What are the self-normalizing subgroups of $S_n$?

If $G$ is a finite group and $H$ is a normal subgroup of $G$,then prove that $o(G/H)=o(G)/o(H).$

Find a subgroup of $S_n$, given its normalizer

Normal Subgroups of $O(n)$

Group theory $G \triangleright H , H \cong \mathbb{Z}, G/H \cong \mathbb{Z}/ n \mathbb{Z}$.Then Classfication of $G$

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