The Quotient Ultra-Groups (original) (raw)

On the category of ultra-groups

Hacettepe Journal of Mathematics and Statistics, 2017

This article has been prepared based on a new concept of an ultra-group H M which is depend on a group G and its subgroup H. Our aim is to introduce the category of ultra-groups and investigate about some properties of this category.

On the Structure of Ultra-Groups Over a Finite Group

2016

Algebraic structures appear in most branches of mathematics, such as the abstract algebra, universal algebra, varieties and category theory. The identification of algebraic structures is also useful in other fields of science. For instance recognition of algebraic structures in quantum physical systems has been an important tool for their understanding (see[4, 9]). Nowadays, answering to the new questions needs some more new tools. One of the very useful notions in mathematics as well as in computer science is the notion of s-acts (see [3, 5] for more details). We establish a new structure, ultragroup. The concept of an ultra-group is the base of a new branch of studies in algebra and the future researches. In the present work we continue the study of a variant of natural generalization of a notion of transversal in a group to its subgroup (see [1, 7]). In the next section of this article we define the notions which are useful through out this work such as a pair of subsets which ar...

Free ultra-groups, generators and relations

2020

In this paper, we intend to define an ultra-group by its presentation. The attitude of the presentation for a group was the key for us to investigate in this area. Instead of writing whole elements of an ultra-group, we denote it by its generators and the relations among those generators. A general computational approach for finitely presented ultra-groups by quotient ultra-groups and subultra-groups is described and some examples are presented. It is the way that can clarify the structure of an ultra-group quicker than having just a list of elements.

On a new construction in group theory

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2009

This paper continues the investigation of the groups RF(G) introduced and studied in [I. M. Chiswell and T. W. Müller, A class of groups with canonical Rtree action, Springer LNM, to appear]. Two new concepts, that of a test function, and that of a pair of locally incompatible (test) functions are introduced, and their theory is developed. As application, we obtain a number of new quantitative as well as structural results concerning the groups RF(G) and their quotients RF(G)/E(G) modulo the subgroup E(G) generated by the elliptic elements. Among other things, the cardinality of RF(G) is determined, and it is shown that both RF(G) and RF(G)/E(G) contain large free subgroups, and that their abelianizations both contain a large Qvector space as direct summand.

On a property of special groups

1999

Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We give a simple proof of the following result: if H^1(L, G) = {1} for some finitely generated field extension L/k of transcendence degree \ge 3 then H^1(K, G) = {1} for every field extension K/k.

Notes on abelian groups. II

Acta Mathematica Academiae Scientiarum Hungaricae

w 5. p.basic subgroups of arbitrary abelian groups KULIKOV [8] introduced the notion of basic subgroups of abelian p-groups which has proved to be one of the most important notions in the theory of p-groups of arbitrary power. Basic subgroups can be defined in any module over the ring of p-adic integers, or, more generally, over any discrete valuation ring. Here we want to give a generalization of basic subgroups to any group so that it coincides with the old concept whenever the group is primary. In the general case, to every prime p, one can define p-basic subgroups where in the definition the prime p plays a distinguished role. The p-basic subgroups are not isomorphic for different primes, but are uniquely determined (up to isomorphism) by the group and the prime p. We shall see that p-basic subgroups are useful in certain investigations. Let G be an arbitrary (abelian) group l and p an arbitrary, but fixed prime. We call a subset [x~]~ea of G, not containing 0, p-independent, if for any finite subset xl .... ,x~ a relation nlxl-[-... q-nkx1~ EprG

A note about congruences on subsemigroups of groups

Semigroup Forum, 2003

A well known elementary argument shows that a totally disconnected normal subgroup of a connected topological group is central, in [2] K. H. Hofmann has shown that by a skillful application of this argument (or variations of it) a much wider class of interesting centrality results can be obtained. In the present paper we offer a modification of the argument also applying to congruences on subsemigroups of topological groups.

Study of Groups with basic property

Maǧallaẗ ǧāmiʻaẗ al-anbār li-l-ʻulūm al-ṣirfaẗ, 2012

The purpose of this paper is to study the concept of dependence , independence and the basis of some algebraic structure and give the definition of a finite group with basic property and study some of its basic properties .