1 research outputs found
Cayley numbers with arbitrarily many distinct prime factors
A positive integer is a Cayley number if every vertex-transitive graph of
order is a Cayley graph. In 1983, Dragan Maru\v{s}i\v{c} posed the problem
of determining the Cayley numbers. In this paper we give an infinite set of
primes such that every finite product of distinct elements from is a Cayley
number. This answers a 1996 outstanding question of Brendan McKay and Cheryl
Praeger, which they "believe to be the key unresolved question" on Cayley
numbers.
We also show that, for every finite product of distinct elements from
, every transitive group of degree contains a semiregular element