The Non-cancellation group of a direct power of a (finite cyclic)-by-cyclic group

PETER WITBOOI
University of the Western Cape, Private Bag X17, Bellville, 7535, South Africa

Abstract:

For a relatively prime pair of natural numbers $n, u$, let $H=\langle a,b \ \vert \ a^n=1, bab^{-1}=a^{u}\rangle$. For any $k\in {\mathbb{N}}$, let $\chi (H^k )$ be the set of all isomorphism classes of groups $G$ with the property that $G\times {\mathbb{Z}}\simeq H^k \times {\mathbb{Z}}$.
The set $\chi (H^k )$ carries a certain group structure, see [P. Witbooi, Generalizing the Hilton-Mislin genus group, J. Algebra 239 No. 1 (2001), 327-339]. In this talk we compute the group $\chi (H^k )$.