Finite groups close to Frobenius groups. (English. Russian original) Zbl 1516.20042

Wei, X.; Zhurtov, A. Kh.; Lytkina, D. V.; Mazurov, V. D.

Sib. Math. J. 60, No. 5, 805-809 (2019); translation from Sib. Mat. Zh. 60, No. 5, 1035-1040 (2019).

Summary: We study finite nonsoluble generalized Frobenius groups; i.e., the groups \(G\) with a proper nontrivial normal subgroup \(F\) such that each coset \(Fx\) of prime order \(p,\) as an element of the quotient group \(G/F\), consists only of \(p\)-elements. The particular example of such a group is a Frobenius group, given that \(F\) is the Frobenius kernel of \(G\), and also the Camina group.

MSC:

20D25	Special subgroups (Frattini, Fitting, etc.)
20D15	Finite nilpotent groups, \(p\)-groups

Keywords:

Frobenius group; generalized Frobenius group; kernel; complement; Camina group

References:

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