The Schur multiplicator of metacyclic groups

Abstract

The Schur multiplicator H 2 G {H_2}G of a (finite) metacyclic group G G is computed with the help of the Lyndon spectral sequence. The order of H 2 G {H_2}G is a useful invariant of G G . A metacyclic group with vanishing Schur multiplicator can be presented with two generators and two relators. A simple description of the totality of these groups is given and all such p p -groups are classified.