Finitely Generated Groups G such that G/Z(G) ≈ C p × C p

Abstract

Finite groups G such that G/Z(G) ≈ C 2 × C 2 where C 2 denotes a cyclic group of order 2 and Z(G) is the center of G were studied in [5] and were used to classify finite loops with alternative loop algebras. In this paper we extend this result to finitely generated groups such that G/Z(G) ≈ C p × C p where C p denotes a cyclic group of prime order p and provide an explicit description of all such groups.