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Generalized Frobenius groups

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Abstract

A pair (G. K) in whichG is a finite group andK◃G, 1<K<G, is said to satisfy (F2) if |C G (x)|=|C G/K (xK)| for allx∈G/K. First we survey all the examples known to us of such pairs in whichG is neither ap-group nor a Frobenius group with Frobenius kernelK. Then we show that under certain restrictions there are, essentially, all the possible examples.

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Author notes

  1. David Chillag

    Present address: Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

Authors and Affiliations

  1. Department of Mathematics, University of Hawaii at Manoa, 96822, Honolulu, HI, USA

    David Chillag & I. D. MacDonald

Authors
  1. David Chillag
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  2. I. D. MacDonald
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Chillag, D., MacDonald, I.D. Generalized Frobenius groups. Israel J. Math. 47, 111–122 (1984). https://doi.org/10.1007/BF02760510

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  • DOI: https://doi.org/10.1007/BF02760510

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