JournalsrmiVol. 18, No. 3pp. 747–759

Some questions on quasinilpotent groups and related classes

  • María Jesús Iranzo

    Universitat de València, Burjassot (Valencia), Spain
  • Juan Medina

    Universidad Politécnica de Cartagena, Spain
  • Francisco Pérez-Monasor

    Universitat de València, Burjassot (Valencia), Spain
Some questions on quasinilpotent groups and related classes cover
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Abstract

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

Cite this article

María Jesús Iranzo, Juan Medina, Francisco Pérez-Monasor, Some questions on quasinilpotent groups and related classes. Rev. Mat. Iberoam. 18 (2002), no. 3, pp. 747–759

DOI 10.4171/RMI/335