On the total component and the torsion part of the partial Schur multiplier

摘要

In This paper, we provide a description of the torsion parts for the components in the partial Schur multiplier pM(G) of a group G. This allows us to classify the finite groups and finitely generated abelian groups having partial Schur multiplier consisting only of trivial components. Also the study of the torsion parts of pM(G) permits us to characterize finite groups for which the total components of PM(G) are isomorphic to the multiplicative group of the base field.