Finite Groups Close to Frobenius Groups

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

doi:10.1134/S0037446619050045

Finite Groups Close to Frobenius Groups

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

Section of Algebra and Mathematical Logic

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	805-809
Number of pages	5
Journal	Siberian Mathematical Journal
Volume	60
Issue number	5
DOIs	https://doi.org/10.1134/S0037446619050045
Publication status	Published - 1 Sep 2019

Keywords

Camina group
complement
Frobenius group
generalized Frobenius group
kernel

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10.1134/S0037446619050045

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AU - Wei, X.

AU - Zhurtov, A. Kh

AU - Lytkina, D. V.

AU - Mazurov, V. D.

PY - 2019/9/1

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N2 - 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.

AB - 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.

KW - Camina group

KW - complement

KW - Frobenius group

KW - generalized Frobenius group

KW - kernel

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JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

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Finite Groups Close to Frobenius Groups

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Keywords

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