Abstract
We introduce the notion of abelian system on a finite group $G$, as a particular case of the recently defined notion of kernel system (see this Journal, September 2001). Using a famous result of Suzuki on CN-groups, we determine all finite groups with abelian systems. Except for some degenerate cases, they turn out to be special linear group of rank $2$ over fields of characteristic $2$ or Suzuki groups. Our ideas were heavily influenced by [1] and [8].
Citation
Paul Lescot. "Families of solvable Frobenius subgroups in finite groups." Nagoya Math. J. 165 117 - 121, 2002.
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