Abstract
Let H be a subgroup of a group G. The permutizer \(P_G(H)\) is the subgroup generated by all cyclic subgroups of G which permute with H. A subgroup H of a group G is strongly permuteral in G if \(P_U(H)=U\) for every subgroup U of G, such that \(H\le U\le G\). We investigate groups with \(\mathbb {P}\)-subnormal or strongly permuteral Sylow subgroups. Moreover, we prove that groups with all strongly permuteral primary cyclic subgroups are supersoluble.
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Monakhov, V., Sokhor, I. Finite Groups with Permuteral Primary Subgroups. Mediterr. J. Math. 21, 55 (2024). https://doi.org/10.1007/s00009-024-02594-4
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DOI: https://doi.org/10.1007/s00009-024-02594-4