The computation of Schur multiplier and capability of pairs of groups of order p~4

摘要

The homological functors of a group have its foundation in homotopy theory and algebraic K-theory. The Schur multiplier of a group is one of the homological functors while the Schur multiplier of pairs of groups is a continuation of the Schur multiplier of a group. Meanwhile, a pair of groups is capable if the precise center or epicenter of the pair of group is trivial. In this research, the Schur multiplier and capability of pairs of all abelian groups of order p~4 are computed.