Fixed-point-free permutations‎,‎ also known as derangements‎,‎ have been studied for
centuries‎.‎ In particular‎,‎ depending on their applications‎,‎ derangements of prime-power order …

Let G be a transitive permutation group acting on a finite set Ω with| Ω|⩾ 2. An element of G
is said to be a derangement if it has no fixed points on Ω, and by a theorem of Jordan from …

We prove that every finite arc-transitive graph of valency twice a prime admits a nontrivial
semiregular automorphism, that is, a non-identity automorphism whose cycles all have the …

Let G be a nontrivial transitive permutation group on a finite set Ω. An element of G is said to
be a derangement if it has no fixed points on Ω. From the orbit counting lemma, it follows that …

A transitive permutation group with no fixed point free elements of prime order is called
elusive. A permutation group on a set Ω is said to be 2-closed if G is the largest subgroup of …

Let G be a transitive permutation group of degree n. We say that G is 2′-elusive if n is
divisible by an odd prime, but G does not contain a derangement of odd prime order. In this …

Let G be a transitive permutation group of degree n with point stabiliser H and let r be a
prime divisor of n. We say that G is r-elusive if it does not contain a derangement of order r …

Let G be a transitive permutation group on a finite set Ω with| Ω|⩾ 2. An element of G is said
to be a derangement if it has no fixed points on Ω. As an easy consequence of the orbit …

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 …

Let $ G\leq {\rm Sym}(\Omega) $ be transitive. Then $ G $ is called\textit {elusive} on
$\Omega $ if it has no fixed point free element of prime order. The\textit {$2 $-closure} of $ G …