All Questions
Tagged with solvable-groups gr.group-theory
8 questions with no upvoted or accepted answers
9
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Which finite solvable groups have solvable automorphism groups?
Is it possible to give a reasonable description of those finite solvable groups $G$ such that $A = {\rm Aut}(G)$ is also solvable?
The central case to deal with is that in which $G$ is a $p$-group of ...
- 44.4k
8
votes
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Groups having exactly two non real-valued irreducible characters
This is an enlarged version of my question on MSE. It was suggested I ask here instead.
Suppose the finite group $G$ has exactly two conjugacy classes that are not self-inverse (a conjugacy class is ...
- 787
4
votes
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A different approach to proving a property of finite solvable groups
Edit: I'd be happy to hear any vague thoughts you might have, however far they may be from a complete solution!
I asked this on math.stackexchange a couple of days ago, but it didn't attract any ...
- 1,433
4
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A big class of finite groups
During my researches, I've obtained a class of finite groups as follows.
Let $\mathcal{C}$ be the class of all finite groups $G$ such that for every factorization $|G|=ab$ there exists a subgroup $H\...
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4
votes
0
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Derived length in linear groups
If $G$ is a group let $(G^{(m)})_{m \geq 0}$ be the derived series.
If there is some $m$ such that $G^{(m+1)} = G^{(m)}$, call the smallest such $m$ the derived length of $G$.
I am interested in ...
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4
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Abelian-by-cyclic subgroups of exponential growth solvable groups
I am currently looking for a reference to a proof (or counterexample) to the following statement:
Statement: Assume $G$ is a finitely generated solvable group of exponential growth, then there is a ...
- 4,432
4
votes
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Is there any probabilistic characterization for generalized solvable groups?
References: This question is inspired by a conjecture of Alon Amit that is solved by Miklós Abért, Nikolay Nikolov and Dan Segal in the following papers:
(1) On the probability of satisfying a word in ...
user82740
1
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Irreducible characters of a semi-direct product with a p-group
Suppose G is a semi-direct product of P with H where P is a (non-abelian) p-group and G is solvable. I wonder what can be said about the irreducible characters of G given information about the ...
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