Golod-Shafarevich groups: a survey

In this paper we survey the main results about Golod-Shafarevich groups and their applications in algebra, number theory and topology.Comment: 54 page

Abstract simplicity of complete Kac-Moody groups over finite fields

Let $G$ be a Kac-Moody group over a finite field corresponding to a generalized Cartan matrix $A$, as constructed by Tits. It is known that $G$ admits the structure of a BN-pair, and acts on its corresponding building. We study the complete Kac-Moody group $\hat{G}$ which is defined to be the closure of $G$ in the automorphism group of its building. Our main goal is to determine when complete Kac-Moody groups are abstractly simple, that is have no proper non-trivial normal subgroups. Abstract simplicity of $\hat{G}$ was previously known to hold when A is of affine type. We extend this result to many indefinite cases, including all hyperbolic generalized Cartan matrices $A$ of rank at least four. Our proof uses Tits' simplicity theorem for groups with a BN-pair and methods from the theory of pro-$p$ groups.Comment: Final version. The statement and the proof of Theorem 5.2 have been corrected. The main result (Theorem 1.1) now holds under slightly stronger restriction

On finite generation of the Johnson filtrations

We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroups of the mapping class group and the automorphism group of a free group is finitely generated in a linear stable range. This was originally proved for the second terms by Ershov and He.Comment: 32 pages. v2: very minor edits. Weaker versions of the results of this paper previously appeared in arXiv:1704.01529 and arXiv:1703.04190v

G. S. Rayshev: Communication Functions of the Modern Artist

The article considers a number of works by Gennady Stepanovich Rayshev as historical and ethnographic sources. The subject of the research is the components of his ethnic consciousness. The goal is to analyze the creative work of the Khanty artist as an original historical and ethnographic source reflecting the ethnic identity, the mentality of the indigenous people of the North and the features of the modern epoch. The research materials are based on the visual, historical and cultural analysis of graphic and pictorial canvases and principal statements of G. S. Rayshev on the problems of artistic creation. The analysis of Rayshev’s creativity shows how the intelligentsia of national minorities retransmits and transforms old and new myths. With the disappearance of traditional culture, the myth has not disappeared. Its forms changed, carriers changed radically, but deep structures were preserved. The myth still exists, although it has changed appearance. When different cultures “meet”, this allows creative personalities to act as mediators between the former mythical array and modernity. Without losing previous ties with their native culture, they are engaged in verbal or pictorial design of the worldview, feelings and thoughts of their ethnic group, and reflect their history and cultural realities. The horizons of artists are much wider compared to ordinary people. They retain ethnic stereotypes, knowledge about life and elements of everyday life that determine the specifics of people’s life longer. Their works have not only artistic value, but also the properties of a historical and ethnographic source. Keywords: graphics, painting, source, G. S. Rayshev, traditional culture, artist, ethno

The congruence subgroup property for AutF2Aut F_2: A group-theoretic proof of Asada's theorem

The goal of this paper is to give a group-theoretic proof of the congruence subgroup property for $Aut(F_2)$, the group of automorphisms of a free group on two generators. This result was first proved by Asada using techniques from anabelian geometry, and our proof is, to a large extent, a translation of Asada's proof into group-theoretic language. This translation enables us to simplify many parts of Asada's original argument and prove a quantitative version of the congruence subgroup property for $Aut(F_2)$.Comment: Final versio

Resource and Energy Efficient Method of Dried Fish Production

The authors of the article propose a method of convective dehydration of fish products, which has an intermittent nature of implementation. The dehydration process consists of the continuous initial phase and following combined periods consisting of phases of drying and relaxation of dehydrated surface layer of the raw material. The necessity of applying relaxation is due to the fact that during the drying process the surface layers that have lost some of the moisture are significantly densified. The size of the capillaries for moisture passing through the surface layers is reduced. Near the surface a layer is formed, which lacks the significant mass of moisture and has low diffusion properties. As a result, the dehydration process of the entire sample slows down. The rational use of relaxation leads to restoring the moisture-conducting properties of the surface layer of fish. The supply of electrical energy to the heating elements is stopped during the relaxation. The minimum circulation rate of the drying agent is maintained in the drying installation. Fresh air with a lower temperature and higher relative humidity than the drying agent is supplied to the drying agent. The conditions in the drying installation restrain external mass transfer and facilitate to the relaxation of the dehydrated surface layer, that is, to the redistribution of moisture in the thickness of the fish. The proposed method of dehydration of fish raw material reduces the cost of electric energy in the production of dried products and provides more rational coolant usage. The final fish products have more attractive appearance due to reduction of tissue deformation as a result of applying the relaxation of dehydrated surface layer