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On Injectors of a Hartley Set of a Finite Group

Nanying Yang

School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China

E-mail Address: yangny@jiangnan.edu.cn

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N.T. Vorob’ev

Department of Mathematics, Masherov Vitebsk State University, Vitebsk 210038, Belarus

E-mail Address: vorobyovnt@tut.by

Corresponding author.

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T.B. Vasilevich

Department of Mathematics, Masherov Vitebsk State University, Vitebsk 210038, Belarus

E-mail Address: tatyana.vasilevich.1992@mail.ru

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https://doi.org/10.1142/S1005386718000470Cited by:0 (Source: Crossref)

Abstract

Let G be a finite group and $H$ be a Hartley set of G. In this paper, we prove the existence and conjugacy of $H$ -injectors of G and describe the characterization of injectors via radicals. As applications, some known results are directly followed.

The first author is supported by an NNSF grant of China (Grant #11301227) and the Natural Science Fundation of Jiangsu Province (Grant #BK20130119). The second author is supported by the State Research Programme “Convergence” of Belarus (2016–2020). The third author is supported by the Belarusian Republican Foundation for Fundamental Research (F17M-064).

Communicated by L.A. Bokut

Keywords:

2010 MSC: 20D10, 20D15