Can we say anything about $\gamma_n(G) \cap \zeta_{n-1}(G)$, where $\gamma_n(G)$ is lower central series and $\zeta_{n-1}(G)$ is upper central series?

score 46 · Answer 8 · 2022-09-16 21:04:12

46

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An alternative notion of nilpotency class for $p$-groups

Published on 16 Sep 2022 - 21:04

score 111 · Answer 9 · 2022-09-18 17:59:35

111

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Lie algebras of upper central series of connected Lie group

Published on 18 Sep 2022 - 17:59

score 56 · Answer 10 · 2022-10-05 10:42:30

56

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Finite group where product of elements of coprime order has product order is nilpotent

Published on 05 Oct 2022 - 10:42

score 86 · Answer 11 · 2022-10-18 17:45:51

86

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Nilpotent of subgroup implies nilpotent of group

Published on 18 Oct 2022 - 17:45

score 37 · Answer 12 · 2022-10-26 11:27:47

37

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Nilpotent ideals in a ring proof

Published on 26 Oct 2022 - 11:27

score 100 · Answer 13 · 2026-03-26 04:14:07

100

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Nilradical in an Artinian ring

Published on 26 Mar 2026 - 4:14

score 133 · Answer 14 · 2022-11-04 21:15:41

133

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Alternative proof that maximal abelian normal subgroups of a nilpotent group are self-centralizing

Published on 04 Nov 2022 - 21:15

score 199 · Answer 15 · 2026-03-25 18:44:17

199

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All maximal subgroups are Sylow subgroups

Published on 25 Mar 2026 - 18:44

List Question

Property of Fitting subgroup: Let $G$ be a finite group and $C:= C_G(F(G))$. Then $O_p(C/C\cap F(G))=1$ for every prime $p$.

Let $N \unlhd G$. Then $G/N$ is nilpotent of class $c\in\Bbb{N}$ iff $c$ is the smallest natural number such that $\gamma_c(G) \subset N$

Proof of Baer's theorem

Classification of nilpotent groups via $p$-groups

Let $G$ be a finite group. Suppose that there exists $n\in\mathbb N_0$ such that $G_n=G_{n+1}$ and $Z(G)=1$. Show that $C(G_n)\subseteq G_n$.

Reference request-dimension of projective representations of nilpotent groups.

Can we say anything about $\gamma_n(G) \cap \zeta_{n-1}(G)$, where $\gamma_n(G)$ is lower central series and $\zeta_{n-1}(G)$ is upper central series?

An alternative notion of nilpotency class for $p$-groups

Lie algebras of upper central series of connected Lie group

Finite group where product of elements of coprime order has product order is nilpotent

Nilpotent of subgroup implies nilpotent of group

Nilpotent ideals in a ring proof

Nilradical in an Artinian ring

Alternative proof that maximal abelian normal subgroups of a nilpotent group are self-centralizing

All maximal subgroups are Sylow subgroups

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