Speaker: Lowell Abrams, George Washington University

Title: Algebraic Structure in a Family of Nim-like Arrays

Abstract: This talk will focus on aspects of the algebraic structure -- called a "quasigroup/loop" structure -- shared by a certain family of recursively generated arrays related to the operation of Nim-addition. How the arrays are constructed and what a quasigroup/loop is will be covered carefully. I will then explain how we can see that each loop in the family is monogenic (generated by a single element in a non-associative fashion), and how this can be used to determine all loop homomorphisms between loops in the family.

This work was developed jointly with Dena Morton of Xavier University.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491