Solomon’s descent algebra is used to define a family of signed measures MW,x for a finite Coxeter group W and x > 0. The measures corresponding to W of type An arise from the theory of card shuffling. Formulas for these measures are obtained and conjectured in special cases. The eigenvalues of the associated Markov chains are computed. By elementary algebraic group theory, choosing a random sem...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. Using the Brauer complex, it is proved that this measure agrees with a second measure on conjugacy classes of the Weyl group in...

More than 20 years ago, B. Fischer [5,6] started his pioneering work on groups generated by a conjugacy class of 3-transpositions, i.e., a conjugacy class of involutions D, such that for all d, e ∈ D, we have that [d, e] = 1 or 〈d, e〉 ' SL2(2). Fischer classified all finite groups G generated by a class of 3-transpositions under the additional assumptions that G′′ = G′ and O2(G) = O3(G) = Z(G) ...