Question

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

score 90 · Answer 1 · 2026-04-14 04:31:53

90

Views

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

Published on 14 Apr 2026 - 4:31

score 341 · Answer 2 · 2026-04-15 11:20:21

341

Views

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

Published on 15 Apr 2026 - 11:20

score 247 · Answer 3 · 2026-04-16 07:12:10

247

Views

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

Published on 16 Apr 2026 - 7:12

score 360 · Answer 4 · 2026-05-10 16:22:15

360

Views

Structure of the Brainball group

Published on 10 May 2026 - 16:22

score 184 · Answer 5 · 2026-04-11 10:46:13

184

Views

Irreducible representations of wreath products of cyclic groups.

Published on 11 Apr 2026 - 10:46

score 206 · Answer 6 · 2026-04-13 14:25:58

206

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 Apr 2026 - 14:25

score 104 · Answer 7 · 2026-05-10 19:25:24

104

Views

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

Published on 10 May 2026 - 19:25

score 168 · Answer 8 · 2026-04-14 08:54:49

168

Views

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

Published on 14 Apr 2026 - 8:54

score 135 · Answer 9 · 2026-04-13 00:38:18

135

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 13 Apr 2026 - 0:38

score 58 · Answer 10 · 2026-04-15 09:26:41

58

Views

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

Published on 15 Apr 2026 - 9:26

score 73 · Answer 11 · 2026-04-16 22:28:28

73

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 16 Apr 2026 - 22:28

score 217 · Answer 12 · 2026-04-16 08:44:13

217

Views

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

Published on 16 Apr 2026 - 8:44

score 69 · Answer 13 · 2026-04-12 07:53:38

69

Views

About the intersection of two commutator subgroups

Published on 12 Apr 2026 - 7:53

score 107 · Answer 14 · 2026-04-14 15:39:12

107

Views

Generalised Symmetric group and Semidirect Product

Published on 14 Apr 2026 - 15:39

score 243 · Answer 15 · 2026-04-11 07:34:52

243

Views

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

Published on 11 Apr 2026 - 7:34

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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