Question

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

score 88 · Answer 1 · 2026-03-25 14:36:46

88

Views

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

Published on 25 Mar 2026 - 14:36

score 339 · Answer 2 · 2026-03-25 14:36:50

339

Views

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

Published on 25 Mar 2026 - 14:36

score 173 · Answer 3 · 2026-03-25 17:20:56

173

Views

Existence of composition series of infinite groups (especially the braid groups and the general linear group)

Published on 25 Mar 2026 - 17:20

score 132 · Answer 4 · 2021-04-05 09:08:06

132

Views

Does there exist a group that can be covered by conjugates of its proper subgroup?

Published on 05 Apr 2021 - 9:08

score 206 · Answer 5 · 2021-04-05 14:47:48

206

Views

Does there always exist a double transversal?

Published on 05 Apr 2021 - 14:47

score 151 · Answer 6 · 2021-04-12 21:45:39

151

Views

Every infinite finitely generated group $G$ has an infinite quotient with only finite proper quotients

Published on 12 Apr 2021 - 21:45

score 77 · Answer 7 · 2021-04-19 06:17:09

77

Views

Are these two infinite groups isomorphic?

Published on 19 Apr 2021 - 6:17

score 178 · Answer 8 · 2021-04-20 14:31:09

178

Views

Show that every proper subgroup is finite

Published on 20 Apr 2021 - 14:31

score 878 · Answer 9 · 2021-04-25 15:37:41

878

Views

A group isomorphism between $\mathbb{Q/Z}$ and $\mathbb{Q/2Z}$

Published on 25 Apr 2021 - 15:37

score 113 · Answer 10 · 2026-03-27 16:16:01

113

Views

How to find a group with generators and relations fulfilling several properties?

Published on 27 Mar 2026 - 16:16

score 236 · Answer 11 · 2021-05-18 20:53:55

236

Views

If $G$ is an infinite group, what can you say about the number of elements of order $n$ in the group?

Published on 18 May 2021 - 20:53

score 112 · Answer 12 · 2021-05-25 00:15:23

112

Views

Ends of a group and Spherical growth function

Published on 25 May 2021 - 0:15

score 89 · Answer 13 · 2021-05-25 21:35:36

89

Views

If $S$ is all finitary permutations of $\Bbb N$ and $A$ is the alternating subgroup, prove $1\lhd A\lhd S$ is the only composition series of $S$

Published on 25 May 2021 - 21:35

score 27 · Answer 14 · 2026-03-26 04:50:34

27

Views

Equivalent definition of nilpotency for infinite groups

Published on 26 Mar 2026 - 4:50

score 49 · Answer 15 · 2021-06-11 17:30:59

49

Views

On a result of Baer on the group $\prod_{n=1}^{\infty} \mathbb{Z}$

Published on 11 Jun 2021 - 17:30

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.

Existence of composition series of infinite groups (especially the braid groups and the general linear group)

Does there exist a group that can be covered by conjugates of its proper subgroup?

Does there always exist a double transversal?

Every infinite finitely generated group $G$ has an infinite quotient with only finite proper quotients

Are these two infinite groups isomorphic?

Show that every proper subgroup is finite

A group isomorphism between $\mathbb{Q/Z}$ and $\mathbb{Q/2Z}$

How to find a group with generators and relations fulfilling several properties?

If $G$ is an infinite group, what can you say about the number of elements of order $n$ in the group?

Ends of a group and Spherical growth function

If $S$ is all finitary permutations of $\Bbb N$ and $A$ is the alternating subgroup, prove $1\lhd A\lhd S$ is the only composition series of $S$

Equivalent definition of nilpotency for infinite groups

On a result of Baer on the group $\prod_{n=1}^{\infty} \mathbb{Z}$

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