Ring epimorphisms often induce silting modules and cosilting modules, termed minimal or cosilting. The aim of this paper is twofold. Firstly, we determine the tilting cotilting over a tame hereditary algebra. In particular, show that large module if only it has an adic as direct summand. Secondly, discuss behavior minimality under ring extensions. We commutative noetherian extend to along any f...

A generalized polygon is a thick incidence geometry of rank 2 such that the girth of the incidence graph is twice the diameter of the incidence graph. These geometries are introduced by Tits [17] for group-theoretical purposes, but became an interesting research object in their own right. For an overview of the geometric study, see [19]. Obviously, the notion of morphism is an important one whe...

We introduce several classes of localizations (idempotent monads) on the category groups and study their properties relations. The most interesting class for us is which coincide with zero derived functors. call them right exact (in sense Keune). prove that a localization L preserves nilpotent finite p-group G map → LG an epimorphism. also some examples (Baumslag’s P-localization respect to set...

We extend the notion of ‘homomorphism-homogeneity’ to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism-homogeneity, giving several examples. We also give further details on related work reported in [Deborah Lockett and John K. Truss, Generic endomorphisms of homogeneous Structures,in ‘Groups and model theory’,...

Let G be the discrete group of orientation preserving diffeomorphisms of the circle, and let H be the subgroup of diffeomorphisms which are the identity in a neighborhood of a given point. It is proved that there is a short exact sequence in the integral homology of groups O-Hz(H)Hz(G) SZ-0. The epimorphism E can be identified with the Euler class for transversally foliated circle bundles. The ...

Let Fn be the free group of rank n and let Aut +(Fn) be its special automorphism group. For an epimorphism π : Fn → G of the free group Fn onto a finite group G we call Γ (G, π) = {φ ∈ Aut+(Fn) | πφ = π} the standard congruence subgroup of Aut+(Fn) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ(G, π) for finite abelian groups G. Moreover, we show that if G is...

ABSTRACT. Torsion and Betti numbers for knots are special cases of more general invariants br and βr, respectively, associated to a finitely generated group G and epimorphism χ : G → Z. The sequence of Betti numbers is always periodic; under mild hypotheses about (G,χ), the sequence br satisfies a linear homogeneous recurrence relation with constant coefficients. Generally, br exhibits exponent...

We consider the relations ≥ and ≥p on the collection of all knots, where k ≥ k (respectively, k ≥p k) if there exists an epimorphism πk → πk of knot groups (respectively, preserving peripheral systems). When k is a torus knot, the relations coincide and k must also be a torus knot; we determine the knots k that can occur. If k is a 2-bridge knot and k ≥p k, then k is a 2-bridge knot with determ...

As a sequel of [4], this paper is devoted to the computation of the digital fundamental group πd 1(O/S;σ) defined by loops in the digital object O for which the digital object S acts as an “obstacle”. We prove that for arbitrary digital spaces the group πd 1(O/S;σ) maps onto the usual fundamental group of the difference of continuous analogues |AO∪S | − |AS |. Moreover, we show that this epimor...

For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, =, ·, α) ordered under anti-order α if there exists an antiorder θ on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder σ on S under α such that q = σ ∪ σ−1. Besides, for regular anti-congruence q on S, a constr...