  Bhatwadekar and Raja Sridharan have constructed a homomorphism of abelian
groups from an orbit set Um(n,A)/E(n,A) of unimodular rows to an Euler class
group. We suggest that this is the last map in a longer exact sequence of
abelian groups. The hypothetical group G that precedes Um(n,A)/E(n,A) in the
sequence is an orbit set of unimodular two by n matrices over the ring A. If n
is at least four we describe a partially defined operation on two by n
matrices. We conjecture that this operation describes a group structure on G if
A has Krull dimension at most 2n-6. We prove that G is mapped onto a subgroup
of Um(n,A)/E(n,A) if A has Krull dimension at most 2n-5.
