Publication status: has appeared in J. Group Theory 6 (2003), 195-207; arXiv: math.RA/0112129

Abstract: Let G be a finitely generated abelian-by-finite group and k a field of
characteristic p (possibly p = 0). The Euler class [k_G] of G over k is defined as the
class of the trivial kG-module in the Grothendieck group G₀(kG). We show that
[k_G] has finite order if and only if every p-regular element of G has infinite
centralizer in G. We also give a lower bound for the order of the Euler class in terms
of suitable finite subgroups of G. This lower bound is derived from a more general result
on finite-dimensional representations of smash products of Hopf algebras.

Electronic preprint: