We prove the freeness conjecture of Broué, Malle and Rouquier for the Hecke algebras associated to most of the primitive complex 2-reflection groups with a single conjugacy class of reflections.

3 Main Results 8 3.1 Mixed-Integer Linear Programming Framework . . . . . . . . . . . . . . . . . . . . . 9 3.2 Initialization of Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Implementing Dynamical Equivalence and Linear Conjugacy . . . . . . . . . . . . . 10 3.4 Implementing Deficiency Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 ...

The aim of this paper is to show that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class. MSC 2000: 20C15

In this paper we show that all Garside groups are strongly translation discrete, that is, the translation numbers of non-torsion elements are strictly positive and for any real number r there are only finitely many conjugacy classes of elements whose translation numbers are less than or equal to r. It is a consequence of the inequality “infs(g) 6 infs(g n) n < infs(g) + 1” for a positive intege...

We prove that the conjugacy problem in a large and natural class of subgroups of right-angled Artin groups (RAAGs), can be solved in linear-time. This class of subgroups has been previously studied by Crisp and Wiest, and independently by Haglund and Wise, as fundamental groups of compact special cube complexes.

We show that every two-dimensional class of topological similarity, and hence every diagonal conjugacy class of pairs, is meager in the group of order preserving bijections of the rationals and in the group of automorphisms of the ordered rational Urysohn space.

This paper introduces the concept of Artin semigroup a large (extra large) type. We prove their injective embedding in corresponding groups type and solvability word conjugacy problem this class semigroups.

We define a notion of effectiveness for subshifts on finitely generated groups. The set of effective subshifts forms a conjugacy class that contains the class of sofic subshifts. We prove that the inclusion is strict for several groups, including amenable groups and groups with more than two ends.

Generalizing results on spin character degrees, we determine for a given conjugacy class of odd type in the double cover of S n spin characters of S n which have the minimal 2-power on this class in their character value. Surprisingly, the Glaisher map plays an important r^ ole here.

Let G be a group. Two elements x, y are said to be in the same z-class if their centralizers are conjugate in G. The conjugacy classes give a partition of G. Further decomposition of the conjugacy classes into z-classes provides an important information about the internal structure of the group. Let V be a vector space of dimension n over a field F of characteristic different from 2. Let B be a...