The Local Structure for Finite Groups with a Large $p$-Subgroup(English, Paperback, Meierfrankenfeld U.)

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The Local Structure for Finite Groups with a Large $p$-Subgroup(English, Paperback, Meierfrankenfeld U.) is written by Meierfrankenfeld U. and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 1470418770 (ISBN 10) and 9781470418779 (ISBN 13).

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 $L$.