Question

Let $\varphi:G\to H$ and $\psi:H\to K$ be homomorphisms. Show that $\ker(\varphi)\unlhd\ker(\psi\circ\varphi).$

score 563 · Answer 1 · 2026-03-28 04:35:48

Let $\varphi:G\to H$ and $\psi:H\to K$ be homomorphisms. Show that $\ker(\varphi)\unlhd\ker(\psi\circ\varphi).$

Published on 28 Mar 2026 - 4:35

score 23 · Answer 2 · 2020-01-27 20:38:26

Let $G$ be finite with $H \leq G$ and $N$ an abelian normal subgroup. Suppose $G=NN_G(H)$ and $H \cap N = \{1\}$. Show that $C_H(N)=1.$

score 106 · Answer 3 · 2020-01-29 21:41:02

106

Views

Internal direct product and quotient product

Published on 29 Jan 2020 - 21:41

score 77 · Answer 4 · 2026-02-23 08:39:33

77

Views

Invariant Sylow subgroups and solvability of finite groups

Published on 23 Feb 2026 - 8:39

score 313 · Answer 5 · 2026-03-26 10:59:38

313

Views

Image of a subgroup under the quotient map

Published on 26 Mar 2026 - 10:59

score 599 · Answer 6 · 2026-03-29 03:23:04

599

Views

Quotient group, group action and quotient space

Published on 29 Mar 2026 - 3:23

score 415 · Answer 7 · 2026-03-28 22:26:32

415

Views

Quotient group acts on quotient space?

Published on 28 Mar 2026 - 22:26

score 23 · Answer 8 · 2020-02-01 10:24:34

23

Views

Regarding a conclusion of a step involving solvable factorgroups and solvable normal subgroup

Published on 01 Feb 2020 - 10:24

score 41 · Answer 9 · 2020-02-02 20:12:15

41

Views

Analyzing the relationship between the normal subgroups $N_1$ and $\langle N_2\cup N_3\rangle$ by way of an isomorphism

Published on 02 Feb 2020 - 20:12

score 78 · Answer 10 · 2026-03-27 00:02:18

78

Views

A short sequence of groups

Published on 27 Mar 2026 - 0:02

score 225 · Answer 11 · 2026-03-26 11:00:11

225

Views

Random Walks on Groups that are neither aperiodic nor irreducible

Published on 26 Mar 2026 - 11:00

score 156 · Answer 12 · 2020-02-07 15:17:52

156

Views

Let $G$ and $H$ be groups. Prove $G \times \{1\}\unlhd G\times H$ and $(G\times H)/(G \times \{1\})\cong H$.

Published on 07 Feb 2020 - 15:17

score 19 · Answer 13 · 2020-02-07 16:38:49

19

Views

Bijection between the set of normal series of the additive group $\mathbb{Z}/a\mathbb{Z}$ and set of finite sequences of integers $>0$

Published on 07 Feb 2020 - 16:38

score 50 · Answer 14 · 2026-03-27 23:20:05

50

Views

Every ﬁnite group G that has a normal Sylow $2$-subgroup is solvable.

Published on 27 Mar 2026 - 23:20

score 212 · Answer 15 · 2026-02-23 08:39:33

212

Views

The coprime action and A-invariant Sylow p-subgroup

Published on 23 Feb 2026 - 8:39

List Question

Let $\varphi:G\to H$ and $\psi:H\to K$ be homomorphisms. Show that $\ker(\varphi)\unlhd\ker(\psi\circ\varphi).$

Let $G$ be finite with $H \leq G$ and $N$ an abelian normal subgroup. Suppose $G=NN_G(H)$ and $H \cap N = \{1\}$. Show that $C_H(N)=1.$

Internal direct product and quotient product

Invariant Sylow subgroups and solvability of finite groups

Image of a subgroup under the quotient map

Quotient group, group action and quotient space

Quotient group acts on quotient space?

Regarding a conclusion of a step involving solvable factorgroups and solvable normal subgroup

Analyzing the relationship between the normal subgroups $N_1$ and $\langle N_2\cup N_3\rangle$ by way of an isomorphism

A short sequence of groups

Random Walks on Groups that are neither aperiodic nor irreducible

Let $G$ and $H$ be groups. Prove $G \times \{1\}\unlhd G\times H$ and $(G\times H)/(G \times \{1\})\cong H$.

Bijection between the set of normal series of the additive group $\mathbb{Z}/a\mathbb{Z}$ and set of finite sequences of integers $>0$

Every ﬁnite group G that has a normal Sylow $2$-subgroup is solvable.

The coprime action and A-invariant Sylow p-subgroup

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