Related papers: Egyptian fractions on groups
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r\geq 2$. This extends the case $r=1$ studied in previous papers \cite{1,8,4}.
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
The notion of a topological Jordan decomposition of a compact element of a reductive p-adic group has proven useful in many contexts. In this paper, we generalise it to groups defined over fairly general discretely-valued fields and prove…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
We prove by using simple number-theoretic arguments formulae concerning the number of elements of a fixed order and the number of cyclic subgroups of a direct product of several finite cyclic groups. We point out that certain multiplicative…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).
We give a topological framework for the study of Sela's limit groups: limit groups are limits of free groups in a compact space of marked groups. Many results get a natural interpretation in this setting. The class of limit groups is known…
We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…
The notion of an Egyptian domain (where the analogue of Egyptian fractions works appropriately), first explored by Guerrieri-Loper-Oman, is extended to the more general notions of generically and locally Egyptian domains. Results from the…
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…
Without assuming the field structure on the additive group of real numbers $\mathbb{R}$ with the usual order $<,$ we explore the fact that every proper subgroup of $\mathbb{R}$ is either closed or dense. This property of subgroups of the…
Egyptian decompositions of 2/D as a sum of two unit fractions are studied by means of certain divisors of D, namely r and s. Our analysis does not concern the method to find r and s, but just why the scribes have chosen a solution instead…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…