On Ternary Rings of Derivable Planes.
Let be a group endowed with a length function , and let be a linear subspace of . We say that satisfies the Haagerup inequality if there exists constants such that, for any , the convolutor norm of on is dominated by times the norm of . We show that, for , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on . If is a word length function on a finitely generated group , we show that,...
We give an estimate for the number of closed loops of given length in the 1-skeleton of a thick euclidean building. This kind of estimate can be used to prove the (RD) property for the subspace of radial functions on groups, as shown in the paper by A. Valette [same issue].
The aim of the paper is to give an effective formula for the calculation of the probability that a random subset of an affine geometry AG(r-1,q) has rank r. Tables for the probabilities are given for small ranks. The expected time to the first moment at which a random subset of an affine geometry achieves the rank r is derived.