TY - JOUR AU - V. N. Kniahina AU - V. S. Monakhov PY - 2020/10/25 Y2 - 2024/03/29 TI - Finite groups with $\Bbb P$-subnormal Sylow subgroup JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 72 IS - 10 SE - Research articles DO - 10.37863/umzh.v72i10.2264 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2264 AB - UDC 512.542Let $\Bbb P$ be the set of all primes. A subgroup $H$ of a finite group $G$ is called $\Bbb P$-subnormal, if either $H = G$ or there exists a chain of subgroups $H = H_0\le H_1\le \ldots \le H_n = G$ such that $|H_i\colon H_{i-1}|\in \Bbb P,$ $1\le i\le n.$We prove that any finite group with a $\Bbb P$-subnormal Sylow $p$-subgroup of odd order is $p$-solvability and any group with $\Bbb P$-subnormal generalized Schmidt subgroups is metanilpotent.  ER -