The note demonstrates that if groups are prime power, normal Hall subgroups exist, suggesting strong structural implications for monolithic groups.
Let [Formula: see text] be a set of prime numbers, [Formula: see text] be a prime and [Formula: see text] be a [Formula: see text]-solvable group. We prove in this note that if [Formula: see text] is [Formula: see text]-power for every nonlinear, monomial and monolithic [Formula: see text], then [Formula: see text] has a normal Hall [Formula: see text]-subgroup.
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Dastouri et al. (2025) studied this question.
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