On a class of Butler groups.
On a generalization of Mycielski's and Znám's conjectures about coset decomposition of Abelian groups
On classes of abelian groups
On covers of abelian groups by cosets
On D'Alembert's functional equation on a Abelian group.
On elementary equivalence of abelian groups
On elongations of totally projective -groups by -projective -groups
On groups in which idempotent reducts form a chain
On multiplicative bases in abelian groups
On p...-High Injectives.
On strongly sum-free subsets of abelian groups
In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists with the following property: for every and any n elements of a group such that the product of any two of them is different from the unit element of the group, there exist l of the such that for and . In this note we answer this question in the affirmative in the first non-trivial case when l=3 and the group is abelian, proving the following result.
On the arity of idempotent reduct of abelian groups
On the arity of idempotent reducts of groups
On the construction of factorial designs using abelian group theory
On the Heyde theorem for discrete Abelian groups
Let X be a countable discrete Abelian group, Aut(X) the set of automorphisms of X, and I(X) the set of idempotent distributions on X. Assume that α₁, α₂, β₁, β₂ ∈ Aut(X) satisfy . Let ξ₁, ξ₂ be independent random variables with values in X and distributions μ₁, μ₂. We prove that the symmetry of the conditional distribution of L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ implies that μ₁, μ₂ ∈ I(X) if and only if the group X contains no elements of order two. This theorem can be considered as an analogue...
On the number of abelian groups of a given order (supplement)
1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, , where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented in [2]....
On the structure of sequences with forbidden zero-sum subsequences
We study the structure of longest sequences in which have no zero-sum subsequence of length n (or less). We prove, among other results, that for and d arbitrary, or and d = 3, every sequence of c(n,d)(n-1) elements in which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where and .
On the Theory and Classification of Abelian p-Groups.
On Virtual Properties and Group Extensions.