2 research outputs found
Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups
Let be a Cayley digraph on a group and let
. The Cayley index of is . It has
previously been shown that, if is a prime, is a cyclic -group and
contains a noncyclic regular subgroup, then the Cayley index of is
superexponential in .
We present evidence suggesting that cyclic groups are exceptional in this
respect. Specifically, we establish the contrasting result that, if is an
odd prime and is abelian but not cyclic, and has order a power of at
least , then there is a Cayley digraph on whose Cayley index
is just , and whose automorphism group contains a nonabelian regular
subgroup
On quasiabelian Cayley graphs and graphical doubly regular representations
A Cayley graph of a group G is a graphical doubly regular representatio