Question

Nilpotent Group and Normal Series

score 115 · Answer 1 · 2026-04-13 15:33:34

115

Views

Nilpotent Group and Normal Series

Published on 13 Apr 2026 - 15:33

score 201 · Answer 2 · 2026-04-14 10:21:06

201

Views

Minimal normal subgroup is contained in Centre of group for nilpotent groups

Published on 14 Apr 2026 - 10:21

score 145 · Answer 3 · 2026-04-13 20:49:05

145

Views

How to use the upper central series instead of the lower one in nilpotency proofs

Published on 13 Apr 2026 - 20:49

score 140 · Answer 4 · 2026-04-14 10:11:50

140

Views

Constructing central series

Published on 14 Apr 2026 - 10:11

score 104 · Answer 5 · 2026-04-15 11:49:39

104

Views

Let $G$ be a nilpotent group and $|G| = p_1p_2p_3$ where $p_i$ are different prime numbers. Prove that $G$ is an abelian group.

Published on 15 Apr 2026 - 11:49

score 305 · Answer 6 · 2026-04-12 18:35:30

305

Views

Suppose $T(B)=AB+BA$. Prove that if $A$ is a nilpotent matrix, then $T$ is a nilpotent operator. (Question on Existing Proof)

Published on 12 Apr 2026 - 18:35

score 233 · Answer 7 · 2026-04-14 20:41:13

233

Views

Lower central series of the Unitriangular group $UT(n, \mathbb{Z}_p)$

Published on 14 Apr 2026 - 20:41

score 110 · Answer 8 · 2026-04-15 05:06:34

110

Views

why "this means that $G'' \subset Z(G')$"?

Published on 15 Apr 2026 - 5:06

score 142 · Answer 9 · 2026-04-16 11:45:53

142

Views

If all proper subgroups of $G$ are nilpotent and $G$ is solvable, the $G$ is nilpotent.

Published on 16 Apr 2026 - 11:45

score 38 · Answer 10 · 2026-04-16 20:24:15

38

Views

If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic?

Published on 16 Apr 2026 - 20:24

score 396 · Answer 11 · 2026-04-16 13:59:07

396

Views

If a nilpotent group has an element of prime order $p$, so does its centre.

Published on 16 Apr 2026 - 13:59

score 100 · Answer 12 · 2026-04-14 00:54:56

100

Views

Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.

Published on 14 Apr 2026 - 0:54

score 61 · Answer 13 · 2026-04-12 17:04:49

61

Views

Characterization of nilpotency with normal subgroups

Published on 12 Apr 2026 - 17:04

score 293 · Answer 14 · 2026-04-15 16:20:34

293

Views

If $N$ is a normal subgroup of $G$, show $Z(G)N/N \subset Z(G/N)$

Published on 15 Apr 2026 - 16:20

score 60 · Answer 15 · 2026-04-16 21:37:49

60

Views

If $N$ is normal in $G$, show $Z_{i}(G)N/N \leq Z_{i}(G/N)$ where $Z_{i}(G)$ is the $i$th term in the upper central series for $G$.

Published on 16 Apr 2026 - 21:37

List Question

Nilpotent Group and Normal Series

Minimal normal subgroup is contained in Centre of group for nilpotent groups

How to use the upper central series instead of the lower one in nilpotency proofs

Constructing central series

Let $G$ be a nilpotent group and $|G| = p_1p_2p_3$ where $p_i$ are different prime numbers. Prove that $G$ is an abelian group.

Suppose $T(B)=AB+BA$. Prove that if $A$ is a nilpotent matrix, then $T$ is a nilpotent operator. (Question on Existing Proof)

Lower central series of the Unitriangular group $UT(n, \mathbb{Z}_p)$

why "this means that $G'' \subset Z(G')$"?

If all proper subgroups of $G$ are nilpotent and $G$ is solvable, the $G$ is nilpotent.

If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic?

If a nilpotent group has an element of prime order $p$, so does its centre.

Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.

Characterization of nilpotency with normal subgroups

If $N$ is a normal subgroup of $G$, show $Z(G)N/N \subset Z(G/N)$

If $N$ is normal in $G$, show $Z_{i}(G)N/N \leq Z_{i}(G/N)$ where $Z_{i}(G)$ is the $i$th term in the upper central series for $G$.

Trending Questions

Popular # Hahtags

Popular Questions