A subgroup H of a residually finite-p group G is almost p-closed in G if H has finite p′-index in ̄̄ H, its closure with respect to the pro-p topology on G. We characterise polycyclic residually finite-p groups in which all subgroups are almost p-closed and discuss a few conditions that are sufficient for particular subgroups H to be almost p-closed. We also present, for each prime p, an example...

Let A be an abelian variety in algebraically closed field of characteristic 0. We prove that the expansion by a generic divisible subgroup with same torsion exists provided has few algebraic endomorphisms, namely End ( ) = Z . The resulting theory is NSOP1 and not simple. Note there exist varieties any genus.

A rational Mackey functor M for a compact Lie group G can be viewed as a collection of sheaves on spaces of conjugacy classes of subgroups, one for each closed subgroup H, related by restriction maps only. This in turn may be speciied by giving a suitably continuous family consisting of a Q 0 (W G (H))-module V (H) for each closed subgroup H with restriction maps V (^ K) ?! V (K) whenever K is ...

A residually finite (profinite) group G is just infinite if every non-trivial (closed) normal subgroup of G is of finite index. This paper considers the problem of determining whether a (closed) subgroup H of a just infinite group is itself just infinite. If G is not virtually abelian, we give a description of the just infinite property for normal subgroups in terms of maximal subgroups. In par...

We describe an algebra of meromorphic functions on the Siegel domain genus two which contains modular forms for arithmetic index six subgroup symplectic group, is closed under three canonical derivations domain. The main ingredients our study are moduli enhanced curves, Gauss-Manin connection and vector fields living such spaces.

THEOREM 2. If G is a finite monolithic group with monolith M (in other words, if G is a finite group with a unique minimal normal subgroup M), then Mis a verbal subgroup ofG. These generalize the corresponding results for finite ^-groups established by Weichsel ((4), Theorems 2-1, 2-3). The second answers affirmatively a (privately communicated) question of Sheila Oates. In order to give our de...

In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where V real inner product space, G compact subgroup of the orthogonal group O (V) and D \subset closed convex cone. By using structure triple, refinement shown. special case = ( ) Cauchy-Schwarz obtained.

It is proved that a graph K has an embedding as a regular map on some closed surface if and only if its automorphism group contains a subgroup G which acts transitively on the oriented edges of K such that the stabiliser G e of every edge e is dihedral of order 4 and the stabiliser G v of each vertex Š is a dihedral group the cyclic subgroup of index 2 of which acts regularly on the edges incid...

Let 1 → (K, K1) → (G, NG(K1)) → (Q, Q1) → 1 be a short exact sequence of pairs of finitely generated groups with K strongly hyperbolic relative to the subgroup K1. Let relative hyperbolic boundary of K with respect to K1 contains atleast three distinct parabolic end points and for all g ∈ G there exists k ∈ K such that gK1g −1 = kK1k , then we prove that there exists a quasi-isometric section s...