Abstract
In this paper families of non-nilpotent subgroups covering the non-nilpotent part ofafinitegroupareconsidered.An A5-free grouppossessingoneofthesefamilies issoluble, andsolublegroupswiththispropertyhaveFittinglengthatmostthree.Aboundonthenumber of primes dividing the order of the group is also obtained.
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