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Semipermutable π-subgroups

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Abstract

Let H be a π-subgroup of G, and assume that HQ = QH for every Sylow q-subgroup Q of G for all primes q not dividing |H|. We show that the normal closure H G of H in G has a nilpotent π-complement, and in the case where π consists of just one prime, H G is solvable.

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References

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  1. Mathematics Department, University of Wisconsin, 480 Lincoln Dr., Madison, WI, 53706, USA

    I. M. Isaacs

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  1. I. M. Isaacs
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Correspondence to I. M. Isaacs.

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Isaacs, I.M. Semipermutable π-subgroups. Arch. Math. 102, 1–6 (2014). https://doi.org/10.1007/s00013-013-0604-2

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  • DOI: https://doi.org/10.1007/s00013-013-0604-2

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