The Local Structure For Finite Groups With A Large $p$-subgroup (memoirs Of The American Mathematical Society)
by U. Meierfrankenfeld /
2016 / English / PDF
3.7 MB Download
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 $L$.
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 $L$.
