## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, August 15, 2019 — 10:00 AM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo**

"Computability of Walker's Cancellation Theorem"

We discuss the effectivization of Walker's Cancellation Theorem in group theory, with a focus on uniformity. That is, if we have an indexed collection of instances of sums of finitely generated abelian groups $A_i \oplus G_i \cong A_i \oplus H_i$ and the codes for the isomorphisms between them, then we wish to know to what extent we can give a single procedure that, given an index $i$, produces an isomorphism between $G_i$ and $H_i$. We begin by examining Cohn's classical proof of the theorem and see how much of it is effective. We then show that in a certain case, we are able to show that no computable procedure can exist. We also exhibit some related open problems.

MC 5479

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1