Question

Show that if $K\triangleleft A\times B$ is non-abelian, then at least one of $K\cap A,K\cap B$ is non-trivial.

score 76 · Answer 1 · 2026-03-26 22:55:34

76

Views

Show that if $K\triangleleft A\times B$ is non-abelian, then at least one of $K\cap A,K\cap B$ is non-trivial.

Published on 26 Mar 2026 - 22:55

score 49 · Answer 2 · 2026-03-30 05:26:31

49

Views

Notation $NM/M$ in the second isomorphism theorem

Published on 30 Mar 2026 - 5:26

score 105 · Answer 3 · 2023-04-15 23:34:47

105

Views

Confusion in the definition of normal subgroup

Published on 15 Apr 2023 - 23:34

score 147 · Answer 4 · 2026-03-26 19:03:59

147

Views

Solvable-by-finite groups

Published on 26 Mar 2026 - 19:03

score 136 · Answer 5 · 2026-03-26 22:58:23

136

Views

If $[G:K] = m$, then prove that $g^m \in K$ for all $g \in G$.

Published on 26 Mar 2026 - 22:58

score 103 · Answer 6 · 2023-04-17 19:33:50

103

Views

For a group $G$, let $C=\{aba^{-1}b^{-1}:a,b\in G\}$, and $H=\langle C\rangle$. Let $\phi_g$ be any inner automorphism of $G$. Show $\phi_g(H) = H.$

Published on 17 Apr 2023 - 19:33

score 86 · Answer 7 · 2026-03-26 22:55:22

86

Views

$K \leq H_1 \leq H_2 \leq G$, and that $K \trianglelefteq G$ and $H_1 \trianglelefteq H_2$. show that $[H_2 : H_1] = [H_2/K : H_1/K]$.

Published on 26 Mar 2026 - 22:55

score 87 · Answer 8 · 2026-03-31 11:59:23

87

Views

How to find all subnormal subgroups of a group?

Published on 31 Mar 2026 - 11:59

score 46 · Answer 9 · 2023-04-20 18:01:39

46

Views

About normal subgroup of a finite quasisimple group

Published on 20 Apr 2023 - 18:01

score 273 · Answer 10 · 2026-03-29 05:43:41

273

Views

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

Published on 29 Mar 2026 - 5:43

score 147 · Answer 11 · 2026-03-26 19:03:06

147

Views

proof that if G is a solvable group then quotient of G is solvable

Published on 26 Mar 2026 - 19:03

score 118 · Answer 12 · 2023-04-27 21:55:38

118

Views

Prove that if $k\mid n$ that there exist subgroup $H\le D_n$ such that $H \cong D_k$.

Published on 27 Apr 2023 - 21:55

score 75 · Answer 13 · 2023-04-28 04:41:55

75

Views

Center of a normal subgroup is also a normal subgroup

Published on 28 Apr 2023 - 4:41

score 110 · Answer 14 · 2026-03-29 05:50:19

110

Views

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

Published on 29 Mar 2026 - 5:50

score 308 · Answer 15 · 2026-03-25 17:52:52

308

Views

Why inner automorphisms; why conjugation? Why not closure under other automorphims?

Published on 25 Mar 2026 - 17:52

List Question

Show that if $K\triangleleft A\times B$ is non-abelian, then at least one of $K\cap A,K\cap B$ is non-trivial.

Notation $NM/M$ in the second isomorphism theorem

Confusion in the definition of normal subgroup

Solvable-by-finite groups

If $[G:K] = m$, then prove that $g^m \in K$ for all $g \in G$.

For a group $G$, let $C=\{aba^{-1}b^{-1}:a,b\in G\}$, and $H=\langle C\rangle$. Let $\phi_g$ be any inner automorphism of $G$. Show $\phi_g(H) = H.$

$K \leq H_1 \leq H_2 \leq G$, and that $K \trianglelefteq G$ and $H_1 \trianglelefteq H_2$. show that $[H_2 : H_1] = [H_2/K : H_1/K]$.

How to find all subnormal subgroups of a group?

About normal subgroup of a finite quasisimple group

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

proof that if G is a solvable group then quotient of G is solvable

Prove that if $k\mid n$ that there exist subgroup $H\le D_n$ such that $H \cong D_k$.

Center of a normal subgroup is also a normal subgroup

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

Why inner automorphisms; why conjugation? Why not closure under other automorphims?

Trending Questions

Popular # Hahtags

Popular Questions