Related papers: On a generalization of monomial groups

We construct new classes of self-similar groups : S-aritmetic groups, affine groups and metabelian groups. Most of the soluble ones are finitely presented and of type FP_{n} for appropriate n.

We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

We show that the class of large-type Artin groups is invariant under isomorphism, in stark contrast with the corresponding situation for Coxeter groups. We obtain this result by providing a purely algebraic characterisation of large-type…

We consider (projectively) linearly sofic groups, i.e. groups which can be approximated using (projective) matrices over arbitrary fields, as a generalization of sofic groups. We generalize known results for sofic groups and groups which…

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…

In this note we study the finite groups whose subgroup lattices are dismantlable.

Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…

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.

We determine which of the finite-type Artin groups are locally indicable, and compute presentations for their commutator subgroups.

For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and `real harmonic functions' with respect to A. We also consider certain groups…

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

We study possibilities for almost $n$-ary and $n$-aritizable theories. Their dynamics both in general case, for $\omega$-categorical theories, and with respect to operations for theories are described.

We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem of a…

We discuss representations of monogenic functions over very regular groups.

Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…

We describe new combinatorial methods for constructing an explicit free resolution of Z by ZG-modules when G is a group of fractions of a monoid where enough least common multiples exist (``locally Gaussian monoid''), and, therefore, for…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \cite{CLM}, where the target group is the mapping class…