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Results tagged with finite-groups
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user 92488
Questions on group theory which concern finite groups.
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Relation between the Frattini property and pronormal subgroups of solvable groups
A subgroup $H$ of $G$ is said to satisfy the Frattini Property if for any subgroup $K$ and $L$ such that $H\leq K \unlhd L$ implies that $L \leq N_L(H)K$.
A subgroup is $H$ is pronormal in $G$ if for …
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Characterisation of finite solvable T-group
Definition: A $T$-group is a group in which normality is a transitive relation.
Definition: A subgroup $H \leq G$ is said to be weakly normal in $G$ if for each $g\in G$, $H^g \leq N_G(H)$ implies tha …
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Pronorm of a finite solvable group
Let $G$ be a group. The pronormaliser of a subgroup $H$ in a group $G$, denoted $P_G(H)$, is defined to be the set of elements of $G$ that pronormalise $H$. That is, $$P_G(H) = \{g \in G \; | \; \exi …
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Maximal subgroups of odd index in $\mathrm{PSL}(3,q)$
Let $G = \mathrm{PSL}(3,q)$ for $q$ odd. I am trying to understand a question that involves understanding the subgroups that contain a Sylow $2$-subgroup, and in particular, are subgroups of odd index …
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