Oval configurations of involutions in symmetric groups

Coset enumeration of groups generated by symmetric sets of involutions

The well-known Todd-Coxeter algorithm [14], which may be viewed as a means of constructing permutation representations of finitely presented groups, remains a primary reference for coset enumeration programs. All the strategies and variants of this algorithm perform essentially the same calculations as the original algorithm, merely choosing different orders in which to process the available in...

Graded Algebras, Anti-involutions, Simple Groups and Symmetric Spaces

Involutions in Weyl Groups

Let G be a split real group with Weyl group W . Let E be an irreducible representation of W . Let V be the stable Lie algebra version of the coherent continuation representation of W . The main result of this paper is a formula for the multiplicity of E in V . The formula involves the position of E in Lusztig’s set ∐ M(G). The paper treats all quasi-split groups G as well.

Involutions of compact Riemannian 4-symmetric spaces

Let G/H be a compact 4-symmetric space of inner type such that the dimension of the center Z(H) of H is at most one. In this paper we shall classify involutions of G preserving H for the case where dimZ(H) = 0, or H is a centralizer of a toral subgroup of G.

Centralisers of Involutions in Black Box Groups

We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the p-core of a black box group of odd characteristic. This special role of involutions suggest that the theory of black box groups reproduces, at a non-determi...