Let S be a 2-group. The rank (normal rank) of S is the maximal dimension of an elementary abelian subgroup (a normal elementary abelian subgroup) of S over Z2. The purpose of this article is to determine the rank and normal rank of S, where S is a Sylow 2-subgroup of the classical groups of odd characteristic.

G. R. Jahanshahloo , F. Hossienzadeh Lotfi , N. Shoja , G. Tohidi , S. Razavyan d a Department of Mathematics, Science & Research Branch, Islamic Azad University, Tehran-Iran b Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh-Iran c Department of Mathematics, Islamic Azad University, Tehran-Center Branch, Tehran-Iran, P.O. Box: 14515-459, [email protected] d De...

Let G be a group and D be a subgroup of G. In this paper we are interested in the description of the lattice L(D; G) = fH j D H Gg of subgroups of G which contain D. We call subgroups H 2 L(D; G) subgroups intermediate between D and G. We are primarily interested in the parametrization of intermediate subgroups and their behaviour with respect to set-theoretic and group-theoretic operations lik...

Abstract. Let G be a connected complex semisimple group, assumed to have trivial center, and let K be a maximal compact subgroup of G. Then G/K, with a fixed G-invariant Riemannian metric, is a Riemannian symmetric space of the complex type. Now let Γ be a discrete subgroup of G that acts freely and cocompactly on G/K. We consider the Segal–Bargmann transform, defined in terms of the heat equat...