Semiregular elements in transitive 2-closed permutation groups of certain degrees

A nonidentity dement 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 (i) 16p, where p not equal 3,7 is a prime, (ii) 4p(3), where p not equal 3 is a prime, (iii) 12pq, where 5 <= p < q are primes, 3p < q and either p not equal 5 or q >= 30, (iv) 18pq, where 5 <= p < q are primes and 2p < q, (v) p(2)qrs, where 2 < p < q < r < s are primes, and (s - 1,r) = 1 or qr < s, and (vi) 4pqrs, where 3 < p < q < r < s are primes, pqr < s, 5 . 7 . 13 inverted iota pqrs and 5 . 31 . 41 inverted iota pqrs. As a corollary, a 2-closed transitive permutation group of degree d <= 100 and different from 72 and 96 contains semiregular elements.