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Permuting the Elements of a Finite Solvable Group

Published online by Cambridge University Press:  20 November 2018

Gerald H. Cliff  and
Akbar H. Rhemtulla
Gerald H. Cliff
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1
Akbar H. Rhemtulla
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1
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Abstract

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The main result in this note is the following

Theorem: Let G be a finite solvable group. There exists a permutation σ of the set G such that {g • σ(g); g∈G} = G if and only if the Sylow 2-subgroup of G is non-cyclic or trivial

Keywords

20D10Finite solvable grouppermutation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 327 - 330
Copyright
Copyright © Canadian Mathematical Society 1979

Footnotes

†

Research partially supported by the National Research Council of Canada.

References

1. Gorenstein, D., Finite Groups, Harper & Row, New York, 1968.Google Scholar