相关论文: L-presentations and branch groups

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

The cogrowth series of a group with respect to a finite generating set is an important combinatorial quantity that seems very difficult to compute exactly, as evidenced by the scarcity of known examples. In this paper, we give a particular…

A group $G$ given by a presentation $G = < \mathcal A \| \mathcal R >$ is called weakly finitely presented if every finitely generated subgroup of $G$, generated by (images of) some words in $\mathcal A^{\pm 1}$, is naturally isomorphic to…

We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying…

We develop a theory of generalized presentations of groups. We give generalized presentations of the symmetric group $\Sigma(X)$ for an arbitrary set $X$ and of the automorphism group of the free group of countable rank, $Aut(F_{\omega})$.

A practical approach is proposed to construct short presentations for Euclidean crystallographic groups in terms of generators and relations. For our purposes a short presentation is the one with a small number of short relators for a given…

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle…

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

We wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of reductive Lie groups, which involve both algebraic and…

Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G \cap GL_m(Z). This is based on a new proof of the result (in more general form…

We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

For an arbitrary countable group G = <A|R> given by its generators A and defining relations R we discuss a specific method for embedding of G into a certain 2-generator group T. Our embedding explicitly lists the images of generators from A…

This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

In a recent paper Cameron, Lakshmanan and Ajith began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable…

If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are…