# Tagged Questions

A solvable group is a group whose derived series terminates in the trivial subgroup.

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### Are all sneaky groups products of Frobenius and 2-Frobenius groups?

I've been stuck thinking about this for a while. Def. Let $G$ be a finite solvable group whose order is divisible by only three primes: $p,q,$ and $r$. Suppose that $G$ has cyclic subgroups of ...
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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 ...
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### Gauss-Wantzel theorem, Fermat primes and solvability of S_n [closed]

Gauss-Wantzel theorem asserts that a polygon with $n$ sides is constructible if and only if $n$ is a product of a power of $2$ and distinct prime Fermat numbers, where the Fermat number of index $k$ ...
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### Schreier's formula and supersolvable groups

A finitely generated profinite group $G$ is said to satisfy Schreier's formula if for every open subgroup $L \leq_o G$ we have $d(L) = (d(G)-1)[G:L] + 1$. Here $d$ stands for the smallest cardinality ...
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### Lucido's three prime lemma

Let G be a finite solvable group. If p,q,r are distinct primes dividing |G|, then G contains an element of order the product of two of these three primes. This is lucido's three prime lemma. I ...
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### Generators of Sylow subgroups

Is there a function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for each finite supersolvable group $G$, and a Sylow subgroup $S \leq G$ we have $d(S) \leq f(d(G))$? Here $d(H)$ denotes the ...
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### Number of generators of the commutator

Can one find a function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for every finite supersolvable group $G$ we have: $d(G') \leq f(d(G))$? Here $d(K)$ is the cardinality of a minimal set of ...
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