Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 47, Number 1-2 (2003), 63-69.
Groups in which Sylow subgroups and subnormal subgroups permute
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 $G$.
Illinois J. Math., Volume 47, Number 1-2 (2003), 63-69.
First available in Project Euclid: 17 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20D40: Products of subgroups
Secondary: 20F19: Generalizations of solvable and nilpotent groups
Ballester-Bolinches, A.; Beidleman, J. C.; Heineken, H. Groups in which Sylow subgroups and subnormal subgroups permute. Illinois J. Math. 47 (2003), no. 1-2, 63--69. doi:10.1215/ijm/1258488138. https://projecteuclid.org/euclid.ijm/1258488138