Abstract
We consider certain properties of finite groups in which the subnormal subgroups permute with all the Sylow subgroups. Such groups are called PST-groups. If $G$ is such a group and $ H_1 / K_1 $ and $ H_2 / K_2 $ are isomorphic abelian chief factors of $G$ such that $ H_1 H_2 \subseteq G' $, then they are operator isomorphic. Moreover, if all the abelian isomorphic chief factors of a PST-group $G$ are operator isomorphic, then all the subnormal subgroups are hypercentrally embedded in $G$.
Citation
A. Ballester-Bolinches. J. C. Beidleman. H. Heineken. "Groups in which Sylow subgroups and subnormal subgroups permute." Illinois J. Math. 47 (1-2) 63 - 69, Spring/Summer 2003. https://doi.org/10.1215/ijm/1258488138
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