Let $p$ be a prime, $G$ a finite $\mathcal{K}_p$-group $S$ a Sylow $p$-subgroup of $G$ and $Q$ a large subgroup of $G$ in $S$ (i.e., $C_G(Q) \leq Q$ and $N_G(U) \leq N_G(Q)$ for $1 \ne U \leq C_G(Q)$). Let $L$ be any subgroup of $G$ with $S\leq L$, $O_p(L)\neq 1$ and $Q\ntrianglelefteq L$. In this paper the authors determine the action of $L$ on the largest elementary abelian normal $p$-reduced $p$-subgroup $Y_L$ of $L$.
| ISBN: | 9781470418779 |
| Publication date: | 30th June 2016 |
| Author: | U Meierfrankenfeld, B Stellmacher, Gernot Stroth |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 342 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Algebraic geometry Algebra |