Schur multiplier
In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H 2 ( G , Z ) {\displaystyle H_{2}(G,\mathbb {Z} )} of a group G. It was introduced by Issai Schur (1904) in his work on projective representations. == Examples and properties == The Schur multiplier M ( G ) {\displaystyle \operatorname {M} (G)} of a finite group G is a finite abelian group whose exponent divides the order of G. If a Sylow p-subgroup of G is cyclic for some p, then the order of M ( G ) {\displaystyle \operatorname {M} (G)} is not divisible by p.