Question

On the finite non-nilpotent group

score 76 · Answer 1 · 2026-03-22 10:36:47

76

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On the finite non-nilpotent group

Published on 22 Mar 2026 - 10:36

score 261 · Answer 2 · 2026-03-19 13:44:53

261

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Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

Published on 19 Mar 2026 - 13:44

score 330 · Answer 3 · 2026-03-19 20:56:57

330

Views

Solvable, non-nilpotent group with nilpotent commutator subgroup

Published on 19 Mar 2026 - 20:56

score 142 · Answer 4 · 2026-03-19 22:06:24

142

Views

When is the automorphism group of a finite $p$-group nilpotent?

Published on 19 Mar 2026 - 22:06

score 115 · Answer 5 · 2026-03-19 23:48:27

115

Views

Locally compact nilpotent group has an open subgroup isomorphic to $\mathbb{R}^n\times K$

Published on 19 Mar 2026 - 23:48

score 384 · Answer 6 · 2026-03-19 11:39:02

384

Views

Let $G$ be a nilpotent group of class 3. Then for every $x ,y ,z$ in $G$, $[x,y,z][y,z,x][z,x,y]=1$.

Published on 19 Mar 2026 - 11:39

score 62 · Answer 7 · 2026-03-19 14:30:40

62

Views

Use an alternative definition for nilpotent groups and show that $D_{8}$ is nilpotent.

Published on 19 Mar 2026 - 14:30

score 314 · Answer 8 · 2026-03-19 18:10:36

314

Views

If $G/Z(G)$ is nilpotent then $G$ is nilpotent

Published on 19 Mar 2026 - 18:10

score 38 · Answer 9 · 2026-03-22 10:22:16

38

Views

Let $Z_i(G)$ be the terms of the upper central series of $G$. Let $H \trianglelefteq G$. Show $Z_i(G)H/H \subseteq Z_i(G/H)$

Published on 22 Mar 2026 - 10:22

score 100 · Answer 10 · 2026-03-19 16:44:07

100

Views

Connected Lie group for which every connected Lie subgroup is simply connected

Published on 19 Mar 2026 - 16:44

score 154 · Answer 11 · 2026-03-22 11:51:36

154

Views

Let $G$ be a finite group and $M,N \lhd G$ such that $M \leq N\cap \Phi(G)$. Then $\frac{N}{M}$ is nilpotent iff $N$ is nilpotent.

Published on 22 Mar 2026 - 11:51

score 354 · Answer 12 · 2026-03-24 11:36:22

354

Views

Nilpotent ring and Nilpotent groups.

Published on 24 Mar 2026 - 11:36

score 532 · Answer 13 · 2026-03-23 23:44:13

532

Views

Let $G$ be a polycyclic group and assume that every finite quotient of $G$ is nilpotent. Then $G$ is nilpotent

Published on 23 Mar 2026 - 23:44

score 90 · Answer 14 · 2026-03-23 21:45:08

90

Views

Show that any finite nilpotent group of square free order is cyclic.

Published on 23 Mar 2026 - 21:45

score 251 · Answer 15 · 2026-03-24 17:26:48

251

Views

Prove $H$ is a proper normal subgroup of $G$ if $H$ is generated by $\{[x,y] \mid x,y \in G\} \cup \{x^p \mid x \in G\}$.

Published on 24 Mar 2026 - 17:26

List Question

On the finite non-nilpotent group

Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

Solvable, non-nilpotent group with nilpotent commutator subgroup

When is the automorphism group of a finite $p$-group nilpotent?

Locally compact nilpotent group has an open subgroup isomorphic to $\mathbb{R}^n\times K$

Let $G$ be a nilpotent group of class 3. Then for every $x ,y ,z$ in $G$, $[x,y,z][y,z,x][z,x,y]=1$.

Use an alternative definition for nilpotent groups and show that $D_{8}$ is nilpotent.

If $G/Z(G)$ is nilpotent then $G$ is nilpotent

Let $Z_i(G)$ be the terms of the upper central series of $G$. Let $H \trianglelefteq G$. Show $Z_i(G)H/H \subseteq Z_i(G/H)$

Connected Lie group for which every connected Lie subgroup is simply connected

Let $G$ be a finite group and $M,N \lhd G$ such that $M \leq N\cap \Phi(G)$. Then $\frac{N}{M}$ is nilpotent iff $N$ is nilpotent.

Nilpotent ring and Nilpotent groups.

Let $G$ be a polycyclic group and assume that every finite quotient of $G$ is nilpotent. Then $G$ is nilpotent

Show that any finite nilpotent group of square free order is cyclic.

Prove $H$ is a proper normal subgroup of $G$ if $H$ is generated by $\{[x,y] \mid x,y \in G\} \cup \{x^p \mid x \in G\}$.

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