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Graphical Regular Representations of Non-Abelian Groups, II

Published online by Cambridge University Press:  20 November 2018

Lewis A. Nowitz  and
Mark E. Watkins
Lewis A. Nowitz
Affiliation:
American Electric Power Service Corporation, 2 Broadway, New York, New York
Mark E. Watkins
Affiliation:
Syracuse University, Syracuse, New York
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The present paper is a sequel to the previous paper bearing the same title by the same authors [3] and which will be hereafter designated by the bold-face Roman numeral I. Further results are obtained in determining whether a given finite non-abelian group G has a graphical regular representation. In particular, an affirmative answer will be given if (|G|, 6) = 1.

Inasmuch as much of the machinery of I will be required in the proofs to be presented and a perusal of I is strongly recommended to set the stage and provide motivation for this paper, an independent and redundant introduction will be omitted in the interest of economy.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1009 - 1018
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Walter, Feit and John G., Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775–1029.Google Scholar
2. Marshall, Hall, Theory of groups (MacMillan, New York, 1959).Google Scholar
3. Lewis A., Nowitz and Mark E., Watkins, Graphical regular representations of non-abelian groups, I, Can. J. Math. 6 (1972), 1–16.Google Scholar
4. Mark E., Watkins, On the action of non-abelian groups on graphs, J. Combinatorial Theory 11 (1971), 95–104.Google Scholar