We construct narcissistic terraces for cyclic groups that have various properties which enable the construction of R-sequencings and strong halfcycles for many non-cyclic abelian groups. Among other results, we show: that an abelian group which is isomorphic to a direct product of cyclic factors such that the number of factors of order congruent to 3 (mod 4) of order at most 79 is at least as l...

A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic if and only if, for any ...

Let P2(G) be defined as the probability that any two elements selected at random from the group G, commute with one another. If G is an Abelian group, P2(G) = 1, so our interest lies in the properties of the commutativity of nonAbelian groups. Particular results include that the maximum commutativity of a non-Abelian group is 5/8, and this degree of commutativity only occurs when the order of t...

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...

‎the number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving gaussian binomial coefficients is presented‎.