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On finite groups with the Cayley invariant property

Published online by Cambridge University Press:  17 April 2009

Cai Heng Li
Cai Heng Li
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands WA 6907, Australia, email: li@maths.uwa.edu.au
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Abstract

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A finite group G is said to have the m-CI property if, for any two Cayley graphs Cay(G, S) and Cay(G, T) of valency m, Cay(G, S) ≅ Cay(G, T) implies Sσ = T for some automorphism σ of G. In this paper, we investigate finite groups with the m-CI property. We first construct groups with the 3-CI property but not with the 2-CI property, and then prove that a nonabelian simple group has the 3-CI property if and only if it is A5. Finally, for infinitely many values of m, we construct Frobenius groups with the m-CI property but not with the nontrivial k-CI property for any k < m.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 253 - 261
Copyright
Copyright © Australian Mathematical Society 1997

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