Stephen P. Humphries

Fusions of Character Tables and Schur Rings of Abelian Groups

If the character table of a finite group H satisfies certain conditions, then the classes and characters of H can fuse to give the character table of a group G of the same order. We investigate the case where H is an abelian group. The theory is developed in terms of the S-rings of Schur and Wielandt. We discuss certain classes of p-groups which fuse from abelian groups and give examples of such groups which do not. We also show that a large class of simple groups do not fuse from abelian groups. The methods to show fusion include the use of extensions which are Camina pairs, but other techniques on S-rings are also developed.

Finite Hurwitz braid group actions on sequences of Euclidean reflections

Abstract We prove that if r 1 ,…, r n are Euclidean reflections corresponding to a linearly independent set of vectors, then the group 〈 r 1 ,…, r n 〉 is finite if and only if the natural Hurwitz braid group action on such ordered sets of reflections has finite orbit and we characterise the orbits for this action. We apply this to give a representation of the braid group on n strands onto the alternating or symmetric groups of degree ( n +1) n −2 (for most n ) which is related to the Morse theory of polynomials, as studied by Catanese, Paluszny and Wajnryb.

Curves of fixed points of trace maps

We study curves of fixed points for certain diffeomorphisms of

SOME LINEAR REPRESENTATIONS OF BRAID GROUPS

{\mathbb{R}}^3

Fusions of Character Tables II: p-Groups

that are induced by automorphisms of a trace algebra. We classify these curves. There is a function

COGROWTH OF GROUPS AND A MATRIX OF REDHEFFER

E

Some subgroups of SL(3, z) generated by involutions

which is invariant under all such trace maps and the level surfaces

Weak Cayley Table Groups II: Alternating Groups and Finite Coxeter Groups

E_t: E=t

A Note on “Conjugacy Classes Outside a Normal Subgroup”

are invariant; a point of

Finite Hurwitz braid group actions for Artin groups

E_t