In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A5-free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.
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Ballester-Bolinches, A., Esteban-Romero, R., Jiang, Q., & Li, X. (2015). On a class of generalised Schmidt groups. Annali Di Matematica Pura Ed Applicata, 194(1), 77–86. https://doi.org/10.1007/s10231-013-0365-3