It was shown by Dikranjan and Shakhmatov in 1992 that if a compact abelian group K admits a proper totally dense pseudocompact subgroup, then K cannot have a torsion closed Gδ-subgroup; moreover this condition was shown to be also sufficient under LH. We prove in ZFC that this condition actually ensures the existence of a proper totally dense subgroup H of K that contains an ω-bounded dense sub...

Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p > 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed isomorphic to a normal (resp. characteris...

We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety G defined over a finite field with a closed subvariety X ⊂ G.

Closed sets have been proven successful in the context of compacted data representation for association rule learning. However, their use is mainly descriptive, dealing only with unlabeled data. This paper shows that when considering labeled data, closed sets can be adapted for classification and discrimination purposes by conveniently contrasting covering properties on positive and negative ex...

For a given closed oriented surface Σ, we introduce chord index homomorphism from subgroup of H1(Σ,Z) to the group indices knot K in Σ×I. Some invariants derived this are discussed.

We show that a closed finite index subgroup of free proalgebraic group is itself group. As an application, we prove the absolute differential Galois one-variable function field over algebraically characteristic zero infinite transcendence degree

If g is an integer ≥ 2, and M is a closed simple 3-manifold such that π1(M) has a subgroup isomorphic to a genus-g surface group and dimZ2 H1(M ;Z2) ≥ max(3g−1, 6), we show that M contains a closed, incompressible surface of genus at most g. As an application we show that if M is a closed orientable hyperbolic 3-manifold such that VolM ≤ 3.08, then dimZ2 H1(M ;Z2) ≤ 5.

Let Γ be a finitely presentable pro-p group such that def(Γ) > 0. If Γ has a nontrivial finitely generated closed normal subgroup N of infinite index then def(Γ) = 1, N is a free pro-p group and Γ/N is virtually free. If π is a finitely presentable group with β (2) 1 (π) = 0 then def(π) ≤ 1, with equality only if c.d.π = 2 or π ∼= Z. (See Theorem 2.5 of [1].) The L-Betti number condition holds ...