Illinois Journal of Mathematics

Groups in which Sylow subgroups and subnormal subgroups permute

A. Ballester-Bolinches, J. C. Beidleman, and H. Heineken

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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

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

First available in Project Euclid: 17 November 2009

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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.

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