“Bulletin Board”

 School of Mathematics - December 9, 2004

Mathematical Lecture

Residual Solvability of Generalized Free Products of Groups

Delaram Kahrobaie
University of St. Andrews Scotland, UK

Dec. 29, 2004
11:00
School of Mathematics, IPM

 
 

Delaram Kahrobaie
University of St. Andrews Scotland, UK


Residual Solvability of Generalized Free Products of Groups

Abstract 1:

In this talk I explore residual solvability of generalized free products of groups; particularly I investigate mostly for two classes of groups: in the first part where the factors are finitely generated nilpotent groups and in the second part I will deal with finitely generated free groups. We show that the generalized free products of finitely generated nilpotent groups are often residually solvable. In the literature residual finiteness of these kinds of structure has been studied by Gilbert Baumslag and Joan Landsman Dyer and number of others. In the second part we I will present some slightly technical theorems on residual solvability of amalgamated products of finitely generated free groups. If time allows I will also discuss some interesting open problems in this area.


Information:

Date: December 29, 2004 at 11:00
Place: Lecture Hall, Niavaran Bldg., Niavaran Square, Tehran, Iran



A Graphic Generalization of Arithmetic

Abstract 2:

In this talk, we extend the classical arithmetic defined over the set of natural numbers N, to the set of all finite directed connected multigraphs having a pair of distinguished vertices. Specifically, we introduce a model F on the set of such graphs, and provide an interpretation of the language of arithmetic L = {0, 1,<,=,+, �} inside F. The resulting model exhibits the property that the standard model on N embeds in F as a submodel, with the directed path of length n playing the role of the standard integer n. We will compare the theory of the larger structure F with classical arithmetic statements that hold in N. For example, we explore the extent to which F enjoys properties like the associativity and commutativity of + and �, distributivity, cancellation and order laws, and decomposition into irreducibles.


Information:

Date: January 1, 2005 at 16:00
Place: Lecture Hall, Niavaran Bldg., Niavaran Square, Tehran, Iran


Some Applications of Polycyclic Groups

Abstract 3:

In this talk I will speak about some algorithmic problems in polycyclic groups and their applications in theoretical computer science. Part of this work is a joint work with B. Eick. The talk should be accessible to both Mathematicians and Computer Scientists.


Information:

Date: January 3, 2005 at 11:00
Place: Lecture Hall, Niavaran Bldg., Niavaran Square, Tehran, Iran
 
 
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