Question

Showing $Z(H\wr K)=1$, for abelian $H\neq 1$ and arbitrary, infinite $K$.

score 87 · Answer 1 · 2021-03-30 11:40:45

87

Views

Showing $Z(H\wr K)=1$, for abelian $H\neq 1$ and arbitrary, infinite $K$.

Published on 30 Mar 2021 - 11:40

score 338 · Answer 2 · 2021-04-01 15:06:40

338

Views

Showing that the restricted wreath product $\Bbb Z\wr\Bbb Z$ is finitely generated.

Published on 01 Apr 2021 - 15:06

score 244 · Answer 3 · 2021-04-27 23:28:43

244

Views

Number of elements of order $p$ in the sylow $p$-subgroup of $S_{p^2}$

Published on 27 Apr 2021 - 23:28

score 356 · Answer 4 · 2021-05-16 14:45:51

356

Views

Structure of the Brainball group

Published on 16 May 2021 - 14:45

score 181 · Answer 5 · 2021-05-17 09:25:43

181

Views

Irreducible representations of wreath products of cyclic groups.

Published on 17 May 2021 - 9:25

score 204 · Answer 6 · 2021-08-13 18:02:23

204

Views

Does anything special happen when you replace the direct product in the definition for a wreath product with a central product?

Published on 13 Aug 2021 - 18:02

score 101 · Answer 7 · 2026-03-25 07:45:45

101

Views

The Frattini subgroup of the standard Wreath product of two quasicyclic groups is the group itself.

Published on 25 Mar 2026 - 7:45

score 165 · Answer 8 · 2021-12-23 19:59:55

165

Views

There exist infinite solvable $p$-groups with trivial centre. (Use a hint.)

Published on 23 Dec 2021 - 19:59

score 132 · Answer 9 · 2021-12-29 14:39:29

132

Views

For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.

Published on 29 Dec 2021 - 14:39

score 55 · Answer 10 · 2022-01-09 00:12:42

55

Views

Is it true that $F^*\wr S_n$ is a solvable group, when $n\leq 5$?

Published on 09 Jan 2022 - 0:12

score 70 · Answer 11 · 2022-04-17 19:54:08

70

Views

Let $G$ be a non abelian simple group. Show that ${\rm Aut}(G^n)$ is isomorphic to ${\rm Aut}(G) \wr{\rm Sym}(n).$

Published on 17 Apr 2022 - 19:54

score 214 · Answer 12 · 2022-05-06 10:10:33

214

Views

Is $S_2 \wr S_k$ contained in $(S_a \times S_b) \wr S_{k-1}$?

Published on 06 May 2022 - 10:10

score 66 · Answer 13 · 2022-07-13 11:26:48

66

Views

About the intersection of two commutator subgroups

Published on 13 Jul 2022 - 11:26

score 104 · Answer 14 · 2022-08-01 18:06:02

104

Views

Generalised Symmetric group and Semidirect Product

Published on 01 Aug 2022 - 18:06

score 240 · Answer 15 · 2022-08-12 01:24:02

240

Views

Krohn-Rhodes decomposition for transformations over $\{0,1\}$

Published on 12 Aug 2022 - 1:24

List Question

Showing $Z(H\wr K)=1$, for abelian $H\neq 1$ and arbitrary, infinite $K$.

Showing that the restricted wreath product $\Bbb Z\wr\Bbb Z$ is finitely generated.

Number of elements of order $p$ in the sylow $p$-subgroup of $S_{p^2}$

Structure of the Brainball group

Irreducible representations of wreath products of cyclic groups.

Does anything special happen when you replace the direct product in the definition for a wreath product with a central product?

The Frattini subgroup of the standard Wreath product of two quasicyclic groups is the group itself.

There exist infinite solvable $p$-groups with trivial centre. (Use a hint.)

For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.

Is it true that $F^*\wr S_n$ is a solvable group, when $n\leq 5$?

Let $G$ be a non abelian simple group. Show that ${\rm Aut}(G^n)$ is isomorphic to ${\rm Aut}(G) \wr{\rm Sym}(n).$

Is $S_2 \wr S_k$ contained in $(S_a \times S_b) \wr S_{k-1}$?

About the intersection of two commutator subgroups

Generalised Symmetric group and Semidirect Product

Krohn-Rhodes decomposition for transformations over $\{0,1\}$

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