It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the approximations of locally compact groups by more general finite algebraic systems are investigated. It is proved that the approximation of locally compact groups b...

We answer in the negative a question of Hartley about representations finite groups, by constructing examples simple groups with arbitrarily large whose endomorphism ring consists just scalars. show as consequence that there are automorphisms locally group SL(∞,Fq) trivial centralizer. The smallest our is A6 q=9.

The following basic results on infinite locally finite subgroups of a free m-generŽ . 48 ator Burnside group B m, n of even exponent n, where m ) 1 and n G 2 , n is divisible by 29, are obtained: A clear complete description of all infinite groups that Ž . Ž . are embeddable in B m, n as maximal locally finite subgroups is given. Any Ž . infinite locally finite subgroup L of B m, n is contained...

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C∗-algebras. The concept is particularly relevant for Elliott’s program to classify nuclear C∗algebras by K-theory data. We study some of its properties and show that a simple unital C∗-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the...

We discuss the approximability of locally compact groups by finite semigroups and finite quasigroups (latin squares). We show that if a locally compact group G is approximable by finite semigroups, then it is approximable by finite groups, and thus many important groups are not approximable by finite semigroups. This result implies, in particular, the impossibility to simulate the field of real...

The topic of the present paper is the following question. Let G be a locally finite group admitting an automorphism φ of finite order such that the centralizer CG(φ) satisfies certain finiteness conditions. What impact does this have on the structure of the group G? Equivalently, one can ask the same question when φ is an element of G. Sometimes the impact is quite strong and the paper is a sur...

The distinguishing number ∆(X) of a graph X is the least positive integer n for which there exists a function f : V (X) → {0, 1, 2, · · · , n−1} such that no nonidentity element of Aut(X) fixes (setwise) every inverse image f−1(k), k ∈ {0, 1, 2, · · · , n − 1}. All infinite, locally finite trees without pendant vertices are shown to be 2distinguishable. A proof is indicated that extends 2-disti...