The Local Structure for Finite Groups With a Large $p$-Subgroup (Memoirs of the American Mathematical Society)

by U. Meierfrankenfeld, B. Stellmacher, and G. Stroth

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 $L$.

• ISBN13: 9781470418779
• Publish Date: 1 July 2016
• Publish Status: Active
• Publish Country: US
• Imprint: American Mathematical Society
• Format: Paperback
• Pages: 342
• Language: English