SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS

OpenAlex İngilizce

We consider a congruence ${\rho}$ on a group G as a subsemigroup of the direct product $G{\times}G$ . It is well known that a relation ${\rho}$ on G is a congruence if and only if there exists a normal subgroup N of G such that ${\rho}=\{(s,\;t):st^{-1}{\in}N\}$ . In this paper we prove that if G is a finitely presented group, and if N is a normal subgroup of G with finite index, then the congruence ${\rho}=\{(s,\;t):st^{-1}{\in}N\}$ on G is finitely presented.