Finitely Generated Groups $G$ such that $G/Z(G)\simeq C_p\times C_p$

Abstract

Finite groups $G$ such that $G/Z(G)\simeq C_2\times C_2$ where $C_2$ denotes a cyclic group of order 2 and $Z(G)$ is the center of $G$ were studied in \cite{casofinito} and were used to classify finite loops with alternative loop algebras. In this paper we extend this result to finitely generated groups such that $G/Z(G)\simeq C_p\times C_p$ where $C_p$ denotes a cyclic group of prime order $p$ and provide an explicit description of all such groups.

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