Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (?,?)-complex sets, subgroupoid, subgroups and describe important examples symmetric group under sets. Additionally, discuss conjugacy class with respect normal subgroups. We define cosets elaborate upon certain operation analog t...

Subgroups H1 and H2 of a group G are said to be locally conjugate if there is a bijection f : H1 → H2 such that h and f(h) are conjugate in G. We study local conjugacy among subgroups of GL2(Z/pZ), where p is an odd prime, building on Andrew Sutherland’s categorizations of subgroups of GL2(Z/pZ) and local conjugacy among them. We obtain a classification of locally conjugate subgroups of GL2(Z/p...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. A separability hypothesis appears in many general t...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let X = Γ\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Γ-equivariant deformation retractions of D = G/K onto a set D0. We prove that D0 is a spine, having dimension equal to the virtual cohomological dimension of Γ. In fact, there is a (k − 1)-parameter family of such deformation retractions, where k is the number of Γ-con...

This document was provoked by a question on the SEQFAN mailing list, which was passed on to me by Simone Severini. We consider the following four questions. How many subgroups of the symmetric group Sn are generated by • transpositions; • 3-cycles; • transpositions and 3-cycles, • products of pairs of transpositions? For each of the four questions there are three ways of counting the subgroups:...