Questions tagged [solvable-groups]
A solvable group is a group whose derived series terminates in the trivial subgroup.
56 questions
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Decomposition of solvable Lie group
Suppose $G$ is a connected Lie group whose radical is $R$. It is known that the solvable group $R$ can always be decomposed as $R=UT$ where $U$ is a simply-connected normal subgroup of $R$ and $T$ is ...
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Infinite pro-$p$ group of finite solvable length and finite coclass
I was reading about infinite pro-$p$ groups of finite coclass from the book "The Structure of Groups of Prime Power Order" by Leedham-Green and McKay. I asked this question in math....
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Portability of Thompson theorem about solvability to Moufang loops
Say we have a finite Moufang Loop $Q$, $|Q|<\infty$.
There is a theorem proved by Thompson that states:
Group $G$, $|G|<\infty$ is solvable $\iff$ $\forall a, b \in G \langle a, b\rangle$ is ...
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Is every connected solvable group Borel?
Is every connected solvable algebraic group a Borel subgroup of a reductive group? If a counterexample exists, I would ideally like it to be over $\Bbb C$.
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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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Splitting of a finite group with no abelian subfactor in composition series
Let $G$ be a finite group with no abelian subfactor in its composition series.
Is $G$ obtained from simple groups by iterating semidirect products?
(Initially it was asked whether $G$ is a direct ...
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