@article{Kniahina_Monakhov_2020, title={Finite groups with $\Bbb P$-subnormal Sylow subgroup}, volume={72}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2264}, DOI={10.37863/umzh.v72i10.2264}, abstractNote={<p>UDC 512.542</p> <p><br>Let $\Bbb P$ be the set of all primes. <br>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 $|H_i\colon H_{i-1}|\in \Bbb P,$ $1\le i\le n.$<br>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.</p> <p>&nbsp;</p&gt;}, number={10}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Kniahina , V. N. and Monakhov , V. S.}, year={2020}, month={Oct.}, pages={1365 - 1371} }