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# Questions tagged [finite-groups]

Questions on group theory which concern finite groups.

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### Subgroup generated by a subgroup and a conjugate of it

Let $H\leq G$ be groups, and $a\in G$ so that $\langle H,a\rangle=G$. Does it follows that $\langle H\cup aHa^{-1}\rangle$ is a normal subgroup of $G$? My hope is that this is true, and my guess is ...
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### Explicit description of the smallest class of groups, that contains all finite simple groups and is closed under semidirect products

Suppose $\Pi$ is the smallest class of groups satisfying the following conditions: All finite simple groups lie in $\Pi$ If $G \cong H \rtimes K$ and both $H$ and $K$ are in $\Pi$, then $G$ is also ...
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### A question on a result of Imre Ruzsa concerning sum-sets

Th main result of this preprint of Imre Ruzsa implies the following Corollary (Ruzsa): For every $r\in\mathbb N$ there exists a real number $\alpha<1$ and a positive integer $m$ such that for ...
310 views

### Is there some sort of classification of finite groups that force solvability?

Suppose $G$ is a finite group. We will say, that it force solvability if any finite group $H$, such that $G$ is isomorphic to its maximal proper subgroup, is solvable. Does there exist some sort of ...
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### Abstract of talk by Wielandt required

I am searching for Abstracts of short communications of the International Congress of Mathematicians, 1962. In particular, the abstract of Wielandt's talk "Bedingungen für die Konjugiertheit von ...
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The Temperley-Lieb-Jones subfactor planar algebra $\mathcal{TLJ}_{\delta}$ admits the following properties: maximal, it exists for every possible index, i.e. $\delta^2 \in \{4cos^2(\pi/n) \ | \ n \... 1answer 2k views ### Are there infinitely many insipid numbers? A number$n$is called insipid if the groups having a core-free maximal subgroup of index$n$are exactly$A_n$and$S_n$. There is an OEIS enter for these numbers: A102842. There are exactly$486\$ ...

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