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Generalized quaternion groups with the -DCI property
A Cayley digraph Cay(G,S) of a finite group with respect to a subset
of is said to be a CI-digraph if for every Cayley digraph Cay(G,T)
isomorphic to Cay(G,S), there exists an automorphism of such that
. A finite group is said to have the -DCI property for some
positive integer if all -valent Cayley digraphs of are CI-digraphs,
and is said to be a DCI-group if has the -DCI property for all . Let be a generalized quaternion group of order
with an integer , and let have the -DCI
property for some . It is shown in this paper that is
odd, and is not divisible by for any prime . Furthermore,
if is a power of a prime , then has the -DCI
property if and only if is odd, and either or .Comment: 1
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