## ON THE AUTOMORPHISM GROUP OF A HRUSHOVSKl'S PSEUDOPLANE ASSOCIATED TO 5/8 (Model theoretic aspects of the notion of inde...

The automorphism group of Hrushovski's pseudoplane associated to 5/8 is a simple group.

The automorphism group of Hrushovski's pseudoplane associated to 5/8 is a simple group.

Published in Indian Journal of Pure and Applied Mathematics

A graph is symmetric if its automorphism group is transitive on the arc set of the graph. In this paper, we give a complete classification of connected pentavalent symmetric graphs of order 18p, for each prime p. It is shown that, such graphs there exist if and only if p = 2, 7 or 19, and up to isomorphism, there are only four such graphs.

Published in Proceedings of the Steklov Institute of Mathematics

The present paper is devoted to the further development of the discrete theory of Riemann surfaces, which was started in the papers by M. Baker and S. Norine and their followers at the beginning of the century. This theory considers finite graphs as analogs of Riemann surfaces and branched coverings of graphs as holomorphic mappings. The genus of a...

Published in Journal of Mathematical Sciences

A family A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{A} $$\end{document} of non-empty subsets of a set X is called an upfamily, if, for each set A∈A\docu...

Published in European Journal of Mathematics

It is known that the moduli space of smooth Fano–Mukai fourfolds V18\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{18}$$\end{document} of genus 10 has dimension one...

Published in Lobachevskii Journal of Mathematics

For a complete Cartan foliation (M,F) we introduce two algebraic invariants g0(M,F) and g1(M,F) which we call structure Lie algebras. If the transverse Cartan geometry of (M,F) is effective then g0(M,F) = g1(M,F). Weprove that if g0(M,F) is zero then in the category of Cartan foliations the group of all basic automorphisms of the foliation (M,F) ad...

Published in Japanese Journal of Mathematics

We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold of index 1 and genus 10. ...

Published in Algebra and Logic

We prove the following theorem. Let U be a locally finite Suzuki–Higman 2-group with respect to an automorphism group H. Then U and H are representable as the respective unions of ascending chains of finite subgroups U1

Published in Algebra and Logic

Let Γ be a distance regular graph with intersection array {35, 32, 1; 1, 4, 35} and let G = Aut(Γ) act transitively on the set of vertices of the graph Γ. It is shown that G is a {2, 3}-group.

Bicirkulant je graf, ki dopušča avtomorfizem z natanko dvema orbitama vozlišč enake velikosti. V članku so karakterizirani vsi neizomorfni 4-valentni povezavno tranzitivni bicirkulanti. Posledično je izpeljana karakterizacija 4-valentnih ločno tranzitivnih dihedrantov.