Coxeter Groups as Beauville Groups

A Note on Beauville p-Groups

We examine which p-groups of order ≤ p6 are Beauville. We completely classify them for groups of order ≤ p4. We also show that the proportion of 2-generated groups of order p5 which are Beauville tends to 1 as p tends to infinity; this is not true, however, for groups of order p6. For each prime p we determine the smallest non-abelian Beauville p-group.

A new infinite family of non-abelian strongly real Beauville p-groups for every odd prime p

We explicitly construct infinitely many a non-abelian strongly real Beauville p-groups for every prime p. Until very recently only finitely many non-abelian strongly real Beauville p-groups were known and all of these were 2-groups.

New examples of mixed Beauville groups

We generalise a construction of mixed Beauville groups first given by Bauer, Catanese and Grunewald. We go on to give several examples of infinite families of characteristically simple groups that satisfy the hypotheses of our theorem and thus provide a wealth of new examples of mixed Beauville groups.

Complete Growth Series of Coxeter Groups with more than Three Generators

Cohomology and Euler Characteristics of Coxeter Groups

Coxeter groups are familiar objects in many branches of mathematics. The connections with semisimple Lie theory have been a major motivation for the study of Coxeter groups. (Crystallographic) Coxeter groups are involved in Kac-Moody Lie algebras, which generalize the entire theory of semisimple Lie algebras. Coxeter groups of nite order are known to be nite re ection groups, which appear in in...