Groups in the syntactic monoid of a composed code (Q1081706)

It is proved: Let Y and Z be codes (with Z finite) and let \(X=Y\circ Z\). Then every group in \(M(X^*)\), the syntactic monoid of \(X^*\), divides a generalized wreath product \((G_ 1\times...\times G_ n)\square H\), where \(G_ 1,...,G_ n\) are groups dividing \(M(Y^*)\) and H is a group dividing \(M(Z^*)\). For the convenience of the reader all definitions and results needed are summarized and most of the results are proved.