Open Access
October, 2002 Some questions on quasinilpotent groups and related classes
María Jesús Iranzo, Juan Medina, Francisco Pérez-Monasor
Rev. Mat. Iberoamericana 18(3): 747-759 (October, 2002).


In this paper we will prove that if $G$ is a finite group, $X$ a subnormal subgroup of $ X F^*(G)$ such that $X F^*(G)$ is quasinilpotent and $Y$ is a quasinilpotent subgroup of $N_G(X)$, then $Y F^*(N_G(X})$ is quasinilpotent if and only if $Y F^*(G)$ is quasinilpotent. Also we will obtain that $F^*{G}$ controls its own fusion in $G$ if and only if $G=F^*{G}$.


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María Jesús Iranzo. Juan Medina. Francisco Pérez-Monasor. "Some questions on quasinilpotent groups and related classes." Rev. Mat. Iberoamericana 18 (3) 747 - 759, October, 2002.


Published: October, 2002
First available in Project Euclid: 28 April 2003

zbMATH: 1038.20010
MathSciNet: MR1954871

Primary: 20D10 , 20F19

Keywords: Fusion , injector , nilpotent group , quasinilpotent group

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.18 • No. 3 • October, 2002
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