Abstract
We study finite groups G with the property that for any subgroup M maximal in G whose order is divisible by all the prime divisors of |G|, M is supersolvable. We show that any nonabelian simple group can occur as a composition factor of such a group and that, if G is solvable, then the nilpotency length and the rank are arbitrarily large. On the other hand, for every prime p, the p-length of such a group is at most 1. This answers questions proposed by V. Monakhov in The Kourovka Notebook.
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Communicated by John S. Wilson.
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Research supported by Ministerio de Ciencia e Innovación PID-2019-103854GB-100, FEDER funds and Generalitat Valenciana AICO/2020/298.
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Moretó, A. Finite groups whose maximal subgroups of order divisible by all the primes are supersolvable. Monatsh Math 195, 497–500 (2021). https://doi.org/10.1007/s00605-020-01492-7
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DOI: https://doi.org/10.1007/s00605-020-01492-7