Vol. 1 No. 2 (2008): Dedicated to the First International Algebra and Geometry Conference in Armenia

The First International Algebra and Geometry Conference in Armenia, organized by the Yerevan State University and the Khachatur Abovian Armenian State Pedagogical University, took place in Yerevan on 16-20 May, 2007.

Algebraic groups are treated here from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

In this paper we provide an implementable formal algorithm for knowledge bases equivalence verification based on the formal definition of knowledge base given by B. I. Plotkin in his works and also study some important properties of automorphic equivalence of models. In addition we show that notion of automorphic equivalence is much wider than the notion of isomorphism.

In the current paper we announce a positive answer for all prime numbers $n > 997$ to the following problem set by Adian in Kourovka Notebook: Is it true that all proper normal subgroups of the group $B(m, n)$ of prime period $n > 665$ are not free periodic groups? The current result also strengthens a similar result of Olshanskiy for sufficiently large odd numbers $n$ ($n > 10^{77}$).

Earlier we have introduced a definition of strong equality of classical tautologies, according to which two tautologies are equal iff they have the same hardness. The strong equality implies well known equality, but not vice versa. The strong equality is based on the notion of determinitive conjunct, using of which some new deduction system for classical propositional logic were defined. Here the notions of strong equality of tautologies for various logics are suggested and the idea of construction of universal deduction system for various propositional logics is given.

We give a direct proof of the following result: for any real linear operator there exists a basis in which it has a Jordan-Postnikov matrix. This matrix for a real linear operator is determined uniquely up to the order of direct summands on the diagonal.

The First International Algebra and Geometry Conference in Armenia 16-20 May, 2007, Yerevan. The conference was devoted to a variety of topics in algebra, geometry, topology, their applications and related fields. The aim of the conference was to invite well known researchers working in these fields to Armenia, and to establish contacts between them and the scientists working in these fields in Armenia.

The First International Algebra and Geometry Conference in Armenia 16-20 May, 2007, Yerevan. Conference Timetable.

The First International Algebra and Geometry Conference in Armenia 16-20 May, 2007, Yerevan. Conference Abstracts

The First International Algebra and Geometry Conference in Armenia 16-20 May, 2007, Yerevan. Conference Photos by Eugene Plotkin and Vahagn H. Mikaelian

The First International Algebra and Geometry Conference in Armenia 16-20 May, 2007, Yerevan. Conference Printable Poster