On finite groups with the Cayley invariant property

Cai-Heng Li

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    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) congruent to Cay(G, T) implies S-sigma = T for some automorphism sigma 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 A(5). Finally, for infinitely many values of In, we construct Frobenius groups with the m-CI property but not with the nontrivial L-CI property for any k <m.
    Original languageEnglish
    Pages (from-to)253-261
    JournalBulletin of the Australian Mathematical Society
    Publication statusPublished - 1997


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