Abstract
A nonidentity element of a permutation group is said to be semiregular provided all of its cycles in its cycle decomposition are of the same length. It is known that semiregular elements exist in transitive 2-closed permutation groups of square-free degree and in some special cases when the degree is divisible by a square of a prime. In this paper it is shown that semiregular elements exist in transitive 2-closed permutation groups of the following degrees
16p, where
is a prime,
where
is a prime,
12pq, where
are primes,
and either
or
18pq, where
are primes and
where
are primes, and
or qr < s, and
4pqrs, where
are primes, pqr < s,
and
As a corollary, a 2-closed transitive permutation group of degree and different from 72 and 96 contains semiregular elements.