A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS

Title & Authors
A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS
He, Xuanli; Qiao, Shouhong; Wang, Yanming;

Abstract
In [5], Johnson introduced the primitivity of subgroups and proved that a finite group G is supersolvable if every primitive subgroup of G has a prime power index in G. In that paper, he also posed an interesting problem: what a group looks like if all of its primitive subgroups are maximal. In this note, we give the detail structure of such groups in solvable case. Finally, we use the primitivity of some subgroups to characterize T-group and the solvable $\small{PST_0}$-groups.
Keywords
finite groups;primitive subgroups;maximal subgroups;the solvable $\small{PST_0}$-groups;
Language
English
Cited by
1.
PRIMITIVE SUBGROUPS AND PST-GROUPS, Bulletin of the Australian Mathematical Society, 2014, 89, 03, 373
2.
Some subgroup embeddings in finite groups: A mini review, Journal of Advanced Research, 2015, 6, 3, 359
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