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Products of groups and group classes

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Abstract

Letχ be a Schunck class, and let the finite groupG=AB=BC=AC be the product of two nilpotent subgroupsA andB andχ-subgroupC. If for every common prime divisorp of the orders ofA andB the cyclic group of orderp is anχ-group, thenG is anχ-group. This generalizes earlier results of O. Kegel and F. Peterson. Some related results for groups of the formG=AB=AK=BK, whereK is a nilpotent normal subgroup ofG andA andB areχ-groups for some saturated formationχ, are also proved.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Mainz, Saarstrasse 21, D-55099, Mainz, Germany

    Bernhard Amberg

  2. Department of Mathematics, University of the Western Cape, Private Bag X 17, 7535, Belville, South Africa

    Andrew Fransman

Authors
  1. Bernhard Amberg
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  2. Andrew Fransman
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Amberg, B., Fransman, A. Products of groups and group classes. Israel J. Math. 87, 9–18 (1994). https://doi.org/10.1007/BF02772979

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