# Tagged Questions

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0answers
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### What are the rank 3 boolean intervals [H,G], with G simple group?

The rank $n$ boolean lattice $B_{n}$ is the subset lattice of $\{1,2, \dots , n\}$. The lattice $B_{3}$ is the following: Question: What are the rank $3$ boolean intervals of the form $[H,G]$, ...
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### Is there an interval of finite groups, at index n, with strictly more elements than the subgroup lattice of any group, of order n?

Let $G$ be a finite group and $\mathcal{L}(G)$ its subgroup lattice. Let $s(n):= max\{|\mathcal{L}(G)| \text{ for } |G|=n \}$. There is an OEIS page for the sequence $s(n)$: A018216 1, 2, 2, 5, 2, ...
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1answer
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### 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 ...
0answers
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### Generator size for cyclic groups

Let $p$ be prime. Consider $\Bbb Z_{p}$, the cyclic multiplicative group. Is it possible to choose a generator $c$ as small as $O(\log(p))$? (wiki shows $c$ as small as $O(\log^{6}(p))$ is possible ...
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### Computational Ring Theory

I have tried to understand and program CGT algorithms though I am a beginner still. But I never get to hear Computational Ring Theory. Even GAP largely supports Groups Theory. Is there some initiative ...
0answers
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### Example of a group with unsolvable word problem

Today I noticed that the last relator in the 27-relator presentation of a group with unsolvable word problem given in Donald J. Collins: A simple presentation of a group with unsolvable word ...
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1answer
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### 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 ...
1answer
2k views

### How to generate all finite groups of order n? [closed]

I know how to generate all Abelian groups of order n, but how would I generate the others? I can't seem to find anything about this. By "generate", I mean produce the Cayley tables for all groups of ...
4answers
3k views

### Computational Algebra - Where?

I'm on my last semester of a math B.Sc. and about to start studying for a math M.Sc in the same institute. It now seems like a good time to start thinking of a PhD. I'm interested in both algebra and ...
1answer
541 views

### Testing permutations to see if they generate $S_n$

Alright, so a similar question was recently asked about the theoretical bound for generating certain permutations in polynomial time. I had been thinking about a related problem in algorithms (with ...