Finite groups with $\Bbb P$-subnormal Sylow subgroup

• Date: 2020
• Main Authors: Kniahina , V. N., Monakhov , V. S., Княгіна , В. М., Монахов , В. С., Monakhov, Victor
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2264
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 512.542 Let $\Bbb P$ 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...