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On the solvability of regular subgroups in the holomorph of a finite solvable group

    We exhibit infinitely many natural numbers n for which there exists at least one insolvable group of order n, and yet the holomorph of every solvable group of order n has no insolvable regular subgroup. We also solve Problem 19.90(d) in the Kourovka notebook.

    Communicated by E. O’Brien

    AMSC: 20B35, 20F16, 20D05

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    Published: 22 October 2019
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