SUBGROUP ACTIONS AND SOME APPLICATIONS

Equivariant Homotopy of Posets and Some Applications to Subgroup Lattices

In this paper we consider the action of a finite group G on the geometric realization ]CP[ of the order complex CP of a poset P, on which a group G acts as a group of poset automorphisms. For special cases we give the G-homotopy type of ]CPr. Moreover, we provide conditions which imply that the orbit space I CPI/G is homotopy equivalent to the geometric realization of the order complex over the...

SOME APPLICATIONS OF THE p-ADIC ANALYTIC SUBGROUP THEOREM

We use a p-adic analogue of the analytic subgroup theorem of Wüstholz to deduce the transcendence and linear independence of some new classes of p-adic numbers. In particular we give p-adic analogues of results of Wüstholz contained in [20] and generalizations of results obtained by Bertrand in [3, 4].

Dynamics of Subgroup Actions on Homogeneous Spaces of Lie Groups and Applications to Number Theory

Subgroup Discovery Techniques and Applications

This paper presents the advances in subgroup discovery and the ways to use subgroup discovery to generate actionable knowledge for decision support. Actionable knowledge is explicit symbolic knowledge, typically presented in the form of rules, that allow the decision maker to recognize some important relations and to perform an appropriate action, such as planning a population screening campaig...

Symmetric Subgroup Actions on Isotropic Grassmannians

Let G be the group preserving a nondegenerate sesquilinear form B on a vector space V , and H a symmetric subgroup of G of the type G1 × G2. We explicitly parameterize the H-orbits in GrG(r), the Grassmannian of r-dimensional isotropic subspaces of V , by a complete set of H-invariants. We describe the Bruhat order in terms of the majorization relationship over a diagram of these H-invariants. ...