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Suborbit Structure of Permutation $p$-Groups and an Application to Cayley Digraph Isomorphism

Published online by Cambridge University Press:  20 November 2018

Brian Alspach  and
Shaofei Du
Brian Alspach
Affiliation:
Department of Mathematics and Statistics University of Regina Regina, Saskatchewan S4S 0A2
Shaofei Du
Affiliation:
Department of Mathematics Capital Normal University Beijing 100037 People's Republic of China
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Abstract

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Let $P$ be a transitive permutation group of order ${{p}^{m}},\,p$ an odd prime, containing a regular cyclic subgroup. The main result of this paper is a determination of the suborbits of $P$. The main result is used to give a simple proof of a recent result by J. Morris on Cayley digraph isomorphisms.

Keywords

20B2505C60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 161 - 167
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Biggs, N., Algebraic Graph Theory. Cambridge Univ. Press, Cambridge, 1974.Google Scholar
[2] Dixon, J. D. and Mortimer, B., Permutation Groups. Springer-Verlag, New York, 1996.Google Scholar
[3] Huppert, B., Endliche Gruppen I. Springer-Verlag, Berlin, 1967.Google Scholar
[4] Joseph, A., The isomorphism problem for Cayley digraphs on groups of prime-squared order. Discrete Math. 141 (1995), 173–183.Google Scholar
[5] Morris, J., Isomorphic Cayley digraphs on nonisomorphic groups. J. Graph Theory (4) 31 (1999), 345–362.Google Scholar
[6] Neumann, P. M., Finite permutation groups, edge-coloured graphs and matrices. In: Topics in Group Theory and Computation, Academic Press, London, 1973.Google Scholar
[7] Wielandt, H., Permutation Groups, Academic Press, New York, 1966.Google Scholar