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 $G=F^*{G}$.
@article{1051544326,
author = {Iranzo, Mar\'\i a Jes\'us and Medina, Juan and P\'erez-Monasor, Francisco},
title = {Some questions on quasinilpotent groups and related classes},
journal = {Rev. Mat. Iberoamericana},
volume = {18},
number = {1},
year = {2002},
pages = { 747-759},
language = {en},
url = {http://dml.mathdoc.fr/item/1051544326}
}
Iranzo, María Jesús; Medina, Juan; Pérez-Monasor, Francisco. Some questions on quasinilpotent groups and related classes. Rev. Mat. Iberoamericana, Tome 18 (2002) no. 1, pp. 747-759. http://gdmltest.u-ga.fr/item/1051544326/