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Some conditions which almost characterize Frobenius groups

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Abstract

The main result of this paper is the following: LetG be a group with a proper non-trivial normal subgroupH such that each coset ofH distinct fromH is contained in a conjugacy class ofG. IfG is not a Frobenius group with kernelH then one ofH orG/H is ap-group. The hypothesis of this theorem is shown to be equivalent to a condition on characters ofG. The only group the author knows which satisfies this hypothesis and is not either Frobenius or ap-group is one of order 72.

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References

  1. B. Huppert,Endliche Gruppen I, Springer-Verlag, Berlin-Heidelberg-New York, 1967.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of East Anglia, Norwich, England

    A. R. Camina

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  1. A. R. Camina
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Camina, A.R. Some conditions which almost characterize Frobenius groups. Israel J. Math. 31, 153–160 (1978). https://doi.org/10.1007/BF02760546

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  • DOI: https://doi.org/10.1007/BF02760546

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