Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...

Given a finitely presented group G and an epimorphism χ : G→ Z, constraints on the orders of automorphisms F : G→ G such that χ ◦ F = χ are obtained via symbolic dynamics. The techniques provide new obstructions to periodicity for knots and links.

We first give a short group theoretic proof of the following result of Lackenby. If G is a large group, H is a finite index subgroup of G admitting an epimorphism onto a non–cyclic free group, and g is an element of H, then the quotient of G by the normal subgroup generated by g n is large for all but finitely many n ∈ Z. In the second part of this note we use similar methods to show that for e...

‎given an integer $n$‎, ‎we denote by $mathfrak b_n$ and $mathfrak c_n$ the classes of all groups $g$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $g$‎, ‎respectively‎. ‎in this paper we give a characterization for groups in $mathfrak b_n$ and for groups in $mathfrak c_n$‎. ‎we also obtain an arithmetic description of the set of all integers $n$ such that a gr...

A novel and facile strategy is developed to fabricate highly nitrogen-doped graphene (N-graphene) based layered, quasi-two-dimensional nanohybrids with ultrathin nanosheet nanocrystals using a low-temperature, solution processing method for high-performance supercapacitor electrodes. High N doping can be achieved together with one of the lowest oxygen content in chemically reduced graphene and ...

such that f(g(a)) = a for all a ∈ L. Projective lattices are characterized in [3] by four conditions. This talk will discuss two of them that are of current interest. If g in (2) is only required to be order-preserving, it is called an isotone section of the epimorphism (1). We will characterize which lattices L have an isotope section for every epimorphism (1). We will use this to characterize...

Consider a group G and an epimorphism u0 : G → Z inducing a splitting of G as a semidirect product ker(u0)oφ Z with ker(u0) a finitely generated free group and φ ∈ Out(ker(u0)) representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-Maclane 2–complex X equipped with a semiflow ψ, and inspired by McMullen’s T...

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End (RZ) of the additive group RZ, taking any r ∈ R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this case RZ is called an E-group. Obvious examples of E-rings are subrings of Q. However there is a proper class of examples constructed recently, see [8]. E-rings ...

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End (RZ) of the additive group RZ, taking any r ∈ R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this case RZ is called an E-group. Obvious examples of E-rings are subrings of Q. However there is a proper class of examples constructed recently, see [8]. E-rings ...