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On Finite Groups with the Cayley Isomorphism Property, II

✍ Scribed by Cai Heng Li

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
184 KB
Volume
88
Category
Article
ISSN
0097-3165

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✦ Synopsis

For a positive integer m, a group G is said to have the m-DCI property if, for any Cayley digraphs Cay(G, S) and Cay(G, T ) of G of valency m (that is, |S| = |T | =m), Cay(G, S)$Cay(G, T ) if and only if S _ =T for some _ # Aut(G). This paper is one of a series of papers towards characterizing finite groups with the m-DCI property. It is shown that, for infinitely many values of m, there exist Frobenius groups with the m-DCI property but not with the k-DCI property for any k<m. Further, it is conjectured that for relative small values of m, these groups and an explicit list of groups given by C.

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