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On finite groups with the Cayley invariant property
Published online by Cambridge University Press: 17 April 2009
Abstract
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