Email: msvu.ca
Phone: 457-6260
Office: EV379
Research Interests: Combinatorial Group Theory
Most of my research has been in the area of combinatorial group theory. Specifically I have worked in equations in groups collaborating, much of the time, with Prof. Leo P. Comerford, Jr. of Eastern Illinios University in Charleston, Illinois.
Given a group, G, and a free group, F, an equation in G is an expression w(g_1, ..., g_m; x_1,...,x_n)= 1 where w 0 G*F (the free product of G and F). An equation is quadratic when each Avariable@, x_i, occurs in the word, w, exactly twice as x_i and x_i, as x_i and (x_i)^(-1), or as (x_i)^(-1) and (x_i)^(-1). It can be shown that quadratic equations have many interesting properties and that their solution is a relatively tractable process compared to dealing with other classes of equations in groups.
For references on results about free groups and equations in groups see the following papers and their bibliographies:
C.C. Edmunds, On the endomorphism problem for free groups II, Proc. London Math. Soc.(3) 38 (1979) 153-168.
L.P. Comerford, Jr. and C.C. Edmunds, Solutions of equations in free groups, Group Theory: Proc. of the 1987 Singapore Conference, Walter de Gruyter, Berlin, New York (1989) 347-356.
L.P. Comerford, Jr. and C.C. Edmunds, Quadratic equations over free groups and free products, J. Algebra 68 (1981) 276-297.
L.P. Comerford, Jr. and C.C. Edmunds, The solvability of quadratic equations in free products of free groups with cyclic amalgamation, J. Indian Math. Soc. 50 (1986) 213-252.
L.P. Comerford, Jr., C.C. Edmunds and G. Rosenberger, Commutators as powers in free products of groups, Proc. Amer. Math. Soc. 122 (1)(1994) 47-52.
L.P. Comerford, Jr. and C.C. Edmunds, Genus of powers in a free group, Geometric Group Theory, Eds.: Charney/Davis/Shapiro, Walter de Gruyter & Co., Berlin, New York (1995) 67-71.