The size of the solvable residual in finite groups
Silvio Dolfi
Università degli Studi di Firenze, ItalyMarcel Herzog
Tel Aviv University, IsraelGil Kaplan
The Academic College of Tel Aviv-Yaffo, IsraelArieh Lev
The Academic College of Tel-Aviv-Yaffo, Israel
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Abstract
Let be a finite group. The solvable residual of , denoted by , is the smallest normal subgroup of such that the respective quotient is solvable. We prove that every finite non-trivial group with a trivial Fitting subgroup satisfies the inequality , where . The constant in this inequality can not be replaced by a larger constant.
Cite this article
Silvio Dolfi, Marcel Herzog, Gil Kaplan, Arieh Lev, The size of the solvable residual in finite groups. Groups Geom. Dyn. 1 (2007), no. 4, pp. 401–407
DOI 10.4171/GGD/19