Related papers: Growth of groups and wreath products

We give a method for effectively generating generalised loxodromics in subgroups of graph products, using positive words. This has several consequences for the growth of subsets of these groups. In particular, we show that graph products of…

An exhaustive version of the thesis to a talk presented at the Groups \& Algebras in Bicocca Conference (GABY), University of Milano-Bicocca (Milan, Italy), June 17 to June 21, 2024.

We show that there are hereditarily just infinite groups of any subgroup growth type between $n$ and $n^{\log n}$. This is obtained calculating the subgroup growth type of a family of hereditarily just infinite profinite groups obtained via…

Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky, and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various…

We present an accessible introduction to basic results on groups of intermediate growth.

We give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.

We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates…

We describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators between two elements of the group, a notion which leads to…

We present methods of calculating statistics generating functions over the colored permutation groups, and generalizing known theorems from the symmetric groups to general colored permutations groups.

We study the geometry of a class of group extensions, containing permutational wreath products, which we call "permutational extensions". We construct for all natural number k a torsion group with growth function asymptotically…

We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.

This is a brief introduction to the study of growth in groups of Lie type, with $SL_2(\mathbb{F}_q)$ and some of its subgroups as the key examples. They are an edited version of the notes I distributed at the Arizona Winter School in 2016.…

We construct an uncountable family of finitely generated groups of intermediate growth, with growth functions of new type. These functions can have large oscillations between lower and upper bounds, both of which come from a wide class of…

- Synth\`ese des travaux pr\'esent\'es en vue d'une Habilitation \`a Diriger des Recherches - Synthesis of works presented towards the Habilitation degree This is a summary (in French) of my work in number theory, group theory and…

This is a short introduction (in Spanish) to the study of growth in finite groups, with SL_2 as an example. Emphasis is put on developments of the decade 2005--2015, originating partly in combinatorics. Little algebraic-geometrical…

Wreath products of non-discrete locally compact groups are usually not locally compact groups, nor even topological groups. We introduce a natural extension of the wreath product construction to the setting of locally compact groups. As an…

We study the LEF growth function of a finitely generated LEF group $\Gamma$, which measures the orders of finite groups admitting local embeddings of balls in a word metric on $\Gamma$. We prove that any sufficiently smooth increasing…

In this paper, we showed how a group acting regularly and a diagonal group are embedded into the wreath products in there product action using the Cartesian Decomposition.

In this paper we consider groups of the form $G\wr L$, where the set of generators naturally extends the sets of generators of $G$ and $L$, and $L$ admits a Cayley graph that is a tree. We show how one can compute the conjugacy growth…

The subject of growth of groups has been active in the former Soviet Union since the early 50's and in the West since 1968, when articles of \v{S}varc and Milnor have been published, independently. The purpose of this note is to quote a few…