All groups considered in this paper are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as a proper subgroup. He et al. ['A note on primitive subgroups of finite groups', Commun. Korean Math. Soc. 28(1) (2013), 55-62] proved that every primitive subgroup of G has index a power of a prime if and only if G Φ (G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group. ©2013 Australian Mathematical Publishing Association Inc..
CITATION STYLE
Ballester-Bolinches, A., Beidleman, J. C., & Esteban-Romero, R. (2014). Primitive subgroups and PST-groups. Bulletin of the Australian Mathematical Society, 89(3), 373–378. https://doi.org/10.1017/s0004972713000592
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