Schur multiplier

The Schur multiplier is an important concept in group theory, particularly in the study of algebraic topology and the classification of group extensions. It can be understood in the context of central extensions of groups. Given a group \( G \), the Schur multiplier \( M(G) \) is defined as the second homology group of \( G \) with coefficients in the integers, denoted as \( H_2(G, \mathbb{Z}) \).