On the Frobenius problem for .
On the Functional Equation
On the functorial method for studying the lattices of subgroups of finite groups.
On the fundamental double four-spiral semigroup.
On the general theory of m-groups
On the generalised equations of associativity and bisymmetry.
On the Generation of Dyadic Integral Orthogonal Groups.
On the Genus of a Nilpotent Group with Finite Commutator Subgroup.
On the graph labellings arising from phylogenetics
We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
On the graph on a Weyl group being an interval graph.
On the greatest congruence relation contained in an equivalence relation and its applications to the algebraic theory of machines
On the Green polynomial of classical groups.
On the group .
On the group of automorphisms of finite wreath products
On the Group of Norm 1 Elements in a Division Algebra.
On the group of reduced identities of relatively free solvable groups.
On the group S L 2 over orders of arithmetic type.
On the Groups with Abelian Sylow 2-Subgroups.
On the heights of power digraphs modulo
A power digraph, denoted by , is a directed graph with as the set of vertices and as the edge set. In this paper we extend the work done by Lawrence Somer and Michal Křížek: On a connection of number theory with graph theory, Czech. Math. J. 54 (2004), 465–485, and Lawrence Somer and Michal Křížek: Structure of digraphs associated with quadratic congruences with composite moduli, Discrete Math. 306 (2006), 2174–2185. The heights of the vertices and the components of for and are determined....
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...