Revista Matemática Iberoamericana


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Volume 18, Issue 3, 2002, pp. 747–759
DOI: 10.4171/RMI/335

Published online: 2002-12-31

Some questions on quasinilpotent groups and related classes

María Jesús Iranzo[1], Juan Medina[2] and Francisco Pérez-Monasor[3]

(1) Universitat de València, Burjassot (Valencia), Spain
(2) Universidad Politécnica de Cartagena, Spain
(3) Universitat de València, Burjassot (Valencia), Spain

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 $G=F^*{G}$.

Keywords: Nilpotent group, quasinilpotent group, injector, fusion

Iranzo María Jesús, Medina Juan, Pérez-Monasor Francisco: Some questions on quasinilpotent groups and related classes. Rev. Mat. Iberoam. 18 (2002), 747-759. doi: 10.4171/RMI/335