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

Solubility of finite generalized Frobenius groups with the kernel of odd index. (English) Zbl 1457.20019

J. Contemp. Math. Anal., Armen. Acad. Sci. 55, No. 1, 67-70 (2020) and Izv. Nats. Akad. Nauk Armen., Mat. 55, No. 1, 88-92 (2020).
Summary: A finite group \(G\) is said to be a generalized Frobenius group with kernel \(F\), if \(F\) is a proper nontrivial normal subgroup of \(G\) and for every element \(Fx\) of prime order of the quotient group \(G/F\) the coset \(Fx\) of the group \(G\) over \(F\) has only \(p\)-elements for some prime \(p\) depending on \(x\). This article considers generalized Frobenius groups with insoluble kernel. We prove that a quotient group of a generalized Frobenius group over its insoluble kernel is a 2-group.

Cited in 1 Document

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D15 Finite nilpotent groups, \(p\)-groups

Keywords:

generalized Frobenius group; Camina pair
PDFBibTeX XMLCite
\textit{X. B. Wei} et al., J. Contemp. Math. Anal., Armen. Acad. Sci. 55, No. 1, 67--70 (2020; Zbl 1457.20019)
Full Text: DOI

References:

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