Abstract
Let [Formula: see text] be a finite group in which every non-nilpotent maximal subgroup has prime index and [Formula: see text] the largest prime divisor of [Formula: see text], without using the solvability of [Formula: see text] we prove that either the Sylow [Formula: see text]-subgroup of [Formula: see text] is normal or [Formula: see text] has a normal [Formula: see text]-complement.
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