Question

If maximal subgroups of solvable group have equal cores, then they are conjugates

score 304 · Answer 1 · 2026-03-25 23:39:35

304

Views

If maximal subgroups of solvable group have equal cores, then they are conjugates

Published on 25 Mar 2026 - 23:39

score 76 · Answer 2 · 2026-03-29 15:40:28

76

Views

If every subgroup of $G$ is $G^k$ for some k, then $G$ is a cyclic group.

Published on 29 Mar 2026 - 15:40

score 116 · Answer 3 · 2019-10-29 00:34:40

116

Views

Is the hypothesis of $G$ being a finite group necessary in this exercise?

Published on 29 Oct 2019 - 0:34

score 80 · Answer 4 · 2019-10-29 23:46:24

80

Views

Let $G\cong H$. If $\exists g\in G$ s.t. $|g|=n$, then $\exists h\in H$ with $|h|=n$, and if each element of $G$ is finite, then each in $H$ is too.

Published on 29 Oct 2019 - 23:46

score 195 · Answer 5 · 2026-03-26 12:46:10

195

Views

Onto homomorphism and dihedral group

Published on 26 Mar 2026 - 12:46

score 1.6k · Answer 6 · 2019-10-30 03:27:40

1.6k

Views

Character table of direct group product

Published on 30 Oct 2019 - 3:27

score 36 · Answer 7 · 2019-10-30 05:36:09

36

Views

Cofibrations in abelian categories

Published on 30 Oct 2019 - 5:36

score 149 · Answer 8 · 2019-10-30 08:50:20

149

Views

From coset set G/H to group G

Published on 30 Oct 2019 - 8:50

score 144 · Answer 9 · 2019-10-30 10:35:26

144

Views

Maximal subgroups of order $p^3$ in finite simple groups

Published on 30 Oct 2019 - 10:35

score 208 · Answer 10 · 2019-10-30 16:18:42

208

Views

Maximal subgroups of order $pq^2$ in finite simple groups

Published on 30 Oct 2019 - 16:18

score 196 · Answer 11 · 2026-03-30 01:26:39

196

Views

Proofs on the Commutator subhgroups

Published on 30 Mar 2026 - 1:26

score 61 · Answer 12 · 2026-03-28 13:22:11

61

Views

Example of conjugacy class where both are not real.

Published on 28 Mar 2026 - 13:22

score 176 · Answer 13 · 2026-03-28 22:31:00

176

Views

$\text{Aut}(A_6)$ is not split extension of $A_6\cong \text{Inn} A_6$, i.e. $\text{Aut}(A_6) \not \cong A_6 \rtimes ( \mathbb Z_2 \times \mathbb Z_2)$

Published on 28 Mar 2026 - 22:31

score 501 · Answer 14 · 2019-11-01 09:40:01

501

Views

Proof of Mackey's restriction formula for the restriction of an induced rerpesentation

Published on 01 Nov 2019 - 9:40

score 131 · Answer 15 · 2026-04-07 13:46:38

131

Views

central series for a finite $p$-group

Published on 07 Apr 2026 - 13:46

List Question

If maximal subgroups of solvable group have equal cores, then they are conjugates

If every subgroup of $G$ is $G^k$ for some k, then $G$ is a cyclic group.

Is the hypothesis of $G$ being a finite group necessary in this exercise?

Let $G\cong H$. If $\exists g\in G$ s.t. $|g|=n$, then $\exists h\in H$ with $|h|=n$, and if each element of $G$ is finite, then each in $H$ is too.

Onto homomorphism and dihedral group

Character table of direct group product

Cofibrations in abelian categories

From coset set G/H to group G

Maximal subgroups of order $p^3$ in finite simple groups

Maximal subgroups of order $pq^2$ in finite simple groups

Proofs on the Commutator subhgroups

Example of conjugacy class where both are not real.

$\text{Aut}(A_6)$ is not split extension of $A_6\cong \text{Inn} A_6$, i.e. $\text{Aut}(A_6) \not \cong A_6 \rtimes ( \mathbb Z_2 \times \mathbb Z_2)$

Proof of Mackey's restriction formula for the restriction of an induced rerpesentation

central series for a finite $p$-group

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