# Tagged Questions

**4**

votes

**0**answers

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### Generalization of a theorem of Øystein Ore in group theory?

Theorem (Ã˜ystein Ore, 1938): A finite group $G$ is cyclic iff its lattice of subgroups $\mathcal{L}(G)$ is distributive.
Proof: see below.
Let $(H \subset G)$ be an inclusion of finite groups and ...

**5**

votes

**1**answer

166 views

### How hard is it to compute the diameter and the growth function of a finite permutation group of small degree?

Let $G \leq {\rm S}_n$ be a finite permutation group, and let
$S = \{g_1, \dots, g_k\}$ be a generating set for $G$ which is closed
under inversion and which does not contain the identity.
The growth ...

**4**

votes

**1**answer

316 views

### Finding groups of odd order without non-cyclic nilpotent quotients

I hope that my question is appropriate for MO, since it might turn out te be mainly a question about GAP or other group theory software.
Is there an algorithm to produce all non-nilpotent groups ...