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Regularp-groups and words giving rise to commutative group operations

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Abstract

Groups with words which give rise to commutative operations are considered. Finitep-groups with this property are shown to be regular. It is also shown that finitep-groups of class less thanp, among other groups, have this property.

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References

  1. C. D. H. Cooper,Words which give rise to another group operation for a given group, inProc. Internat. Conf. Theory of Groups (Canberra 1965), 221–225. (Lecture Notes in Mathematics, No. 372, Springer-Verlag, Berlin, Heidelberg and New York, 1974).

    Google Scholar 

  2. G. Higman and B. H. Neumann,Groups as groupoids with one law, Publ. Math. Debrecen2 (1951–2), 215–221.

    MathSciNet  Google Scholar 

  3. A. Hulanicki and S. Świerczkowski,On group operations other than xy or yx, Publ. Math. Debrecen9 (1962), 142–148.

    MATH  MathSciNet  Google Scholar 

  4. B. Huppert,Endliche Gruppen I, inErgebnisse der Mathematik und ihrer Grenzgebiete, Band37, Springer-Verlag, Berlin, Heidelberg and New York, 1967.

    Google Scholar 

  5. Avinoam Mann,Regular p-groups, Israel J. Math.10 (1971), 471–477.

    MATH  MathSciNet  Google Scholar 

  6. Anne Penfold Street,Subgroup determining functions on groups, Illinois J. Math.12 (1968), 99–120.

    MATH  MathSciNet  Google Scholar 

  7. Paul M. Weichsel,Regular p-groups and varieties, Math. Z.95 (1967), 223–231.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, University of Melbourne, 3052, Parkville, Victoria, Australia

    J. R. J. Groves

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  1. J. R. J. Groves
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Groves, J.R.J. Regularp-groups and words giving rise to commutative group operations. Israel J. Math. 24, 73–77 (1976). https://doi.org/10.1007/BF02761430

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  • DOI: https://doi.org/10.1007/BF02761430

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