Illinois Journal of Mathematics

Groups in which Sylow subgroups and subnormal subgroups permute

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 $G$.

Article information

Source
Illinois J. Math., Volume 47, Number 1-2 (2003), 63-69.

Dates
First available in Project Euclid: 17 November 2009

https://projecteuclid.org/euclid.ijm/1258488138

Digital Object Identifier
doi:10.1215/ijm/1258488138

Mathematical Reviews number (MathSciNet)
MR2031306

Zentralblatt MATH identifier
1033.20019

Subjects
Primary: 20D40: Products of subgroups
Secondary: 20F19: Generalizations of solvable and nilpotent groups

Citation

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