Conjugacy Class Representatives in the Monster Group

Computing conjugacy class representatives in permutation groups

We describe a significantly improved algorithm for computing the conjugacy classes of a finite permutation group with trivial soluble radical. We rely on existing methods for groups that are almost simple, and we are concerned here only with the reduction of the general case to the almost simple case. Dedicated to Charles Leedham-Green on the occasion of his 65th birthday

On the action of the sporadic simple Baby Monster group on its conjugacy class 2B

We determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster group B on its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 2.Co2. This is one of the first applications of a new general computational technique to enumerate big orbits. Mathematics Subje...

Conjugacy in Thompson’s Group

We present a characterisation of conjugacy in Thompson’s group using the natural action of F on the interval [0, 1]. This characterisation completes the program begun by Brin and Squier [BS01]. Our characterisation also provides another solution to the conjugacy problem in Thompson’s group which was first solved by Guba and Sapir using diagram groups [GS97]. A number of other solutions exist du...

The Fake Monster Formal Group

Conjugacy in Thompson’s Group F

We complete the program begun by Brin and Squier of characterising conjugacy in Thompson’s group F using the standard action of F as a group of piecewise linear homeomorphisms of the unit interval.