24 citations · 87 across the 18 of their papers we have counts for
12 papers · 1 filter
Finite primitive groups and regular orbits of group elements
Simon Guest, Pablo Spiga
We prove that if is a finite primitive permutation group and if is an element of , then either has a cycle of length equal to its order, or for some , and …
Finite primitive permutation groups containing a permutation having at most four cycles
Simon Guest, Cheryl Praeger, Joy Morris +1
We classify the finite primitive groups containing a permutation with at most four cycles (including fixed points) in its disjoint cycle representation.
Affine transformations of finite vector spaces with large orders or few cycles
Simon Guest, Joy Morris, Cheryl Praeger +1
Let V be a d-dimensional vector space over a field of prime order p. We classify the affine transformations of V of order at least p^d/4, and apply this classification to determine…
A remark on the permutation representations afforded by the embeddings of in
Simon Guest, Andrea Previtali, Pablo Spiga
We show that the permutation module over afforded by the action of on its natural module is isomorphic to the permutation module over affor…
Criteria for solvable radical membership via p-elements
Simon Guest, Dan Levy
Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable radical of a finite group can be characterized as the set of all such that is solvable f…
The exact number of r-regular elements in finite exceptional groups
Simon Guest
We calculate the precise number of r-regular elements in the finite exceptional groups. As a corollary we find that the proportion of r-regular elements is at least 3577/18432 and…