On the form of homomorphisms into the differential group \(L^1_s\) and their extensibility (Q1781907)

The \(s\)-th differential group \(L^1_{s}\) is the set of \(s\)-tuples with real or complex components, the first component being nonzero, with product formed as the \(k\)-th derivative (\(k=1,\dots,s\)) of a composite function. The authors consider homomorphisms \(F_s=(1,0,\dots,0,f),\) the last, \(q\)-th (\(q=2,\dots,s\)) component \(f\) being nonzero, from an abelian group into \(L^1_{s}.\) In particular they give a necessary and sufficient conditon for \(F_s\) to be extendable to \(F_{s+1}.\)