Question

The larger the commutator subgroup is, the "less abelian" the group is

score 109 · Answer 1 · 2020-11-05 17:48:56

109

Views

The larger the commutator subgroup is, the "less abelian" the group is

Published on 05 Nov 2020 - 17:48

score 74 · Answer 2 · 2020-11-05 19:05:24

74

Views

Condition that shows when there are elements in $[G,G]$ which are not commutator.(Looking for a proof)

Published on 05 Nov 2020 - 19:05

score 202 · Answer 3 · 2020-11-23 15:05:18

202

Views

Assume $G$ is a finite group such that every maximal subgroup of $G$ is normal in $G$ and for $H \leq G$ we have that $HG’=G$,then show that $H=G$.

Published on 23 Nov 2020 - 15:05

score 90 · Answer 4 · 2020-11-29 12:33:10

90

Views

If $G$ is group with $|G|=p^3$, $p$ prime, then $G'=Z(G)$

Published on 29 Nov 2020 - 12:33

score 35 · Answer 5 · 2020-12-05 16:57:39

35

Views

Prove that $D'_n=\langle x^2\rangle$

Published on 05 Dec 2020 - 16:57

score 85 · Answer 6 · 2020-12-08 22:05:41

85

Views

Let $G$ be a group. Prove that $G'$ is central iff ${\rm Inn}(G)$ is abelian.

Published on 08 Dec 2020 - 22:05

score 55 · Answer 7 · 2020-12-11 09:01:02

55

Views

Proves about $L_n$ (lower central series of a group $G$)

Published on 11 Dec 2020 - 9:01

score 80 · Answer 8 · 2020-12-31 03:36:58

80

Views

The commutator subgroup of a nonabelian simple group $G$ is $G$ itself

Published on 31 Dec 2020 - 3:36

score 109 · Answer 9 · 2021-01-14 17:24:20

109

Views

If $G=⨝_{i\in I} H_i$ and $K\unlhd G$ is perfect, then $K=⨝_{i\in I}(H_i\cap K)$.

Published on 14 Jan 2021 - 17:24

score 33 · Answer 10 · 2021-02-05 00:07:08

33

Views

Why do certain relatively free groups have perfect commutator subgroups?

Published on 05 Feb 2021 - 0:07

score 591 · Answer 11 · 2021-02-15 06:04:12

591

Views

What is the number of degree $1$ representations of a finite group?

Published on 15 Feb 2021 - 6:04

score 218 · Answer 12 · 2021-04-10 15:07:45

218

Views

Number of conjugacy classes of $G/[G,G]$

Published on 10 Apr 2021 - 15:07

score 249 · Answer 13 · 2021-04-11 10:31:50

249

Views

Is it "obvious" that nested commutators generate the derived series?

Published on 11 Apr 2021 - 10:31

score 167 · Answer 14 · 2021-06-08 21:24:34

167

Views

Show ${\rm SL}(n,q)$ is perfect for odd prime power $q>3$.

Published on 08 Jun 2021 - 21:24

score 62 · Answer 15 · 2021-06-24 22:28:03

62

Views

The commutator of the product of 2 groups

Published on 24 Jun 2021 - 22:28

List Question

The larger the commutator subgroup is, the "less abelian" the group is

Condition that shows when there are elements in $[G,G]$ which are not commutator.(Looking for a proof)

Assume $G$ is a finite group such that every maximal subgroup of $G$ is normal in $G$ and for $H \leq G$ we have that $HG’=G$,then show that $H=G$.

If $G$ is group with $|G|=p^3$, $p$ prime, then $G'=Z(G)$

Prove that $D'_n=\langle x^2\rangle$

Let $G$ be a group. Prove that $G'$ is central iff ${\rm Inn}(G)$ is abelian.

Proves about $L_n$ (lower central series of a group $G$)

The commutator subgroup of a nonabelian simple group $G$ is $G$ itself

If $G=⨝_{i\in I} H_i$ and $K\unlhd G$ is perfect, then $K=⨝_{i\in I}(H_i\cap K)$.

Why do certain relatively free groups have perfect commutator subgroups?

What is the number of degree $1$ representations of a finite group?

Number of conjugacy classes of $G/[G,G]$

Is it "obvious" that nested commutators generate the derived series?

Show ${\rm SL}(n,q)$ is perfect for odd prime power $q>3$.

The commutator of the product of 2 groups

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