SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS

Title & Authors
SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS
Ayik, Gonca; Caliskan, Basri;

Abstract
We consider a congruence $\small{{\rho}}$ on a group G as a subsemigroup of the direct product $\small{G{\times}G}$. It is well known that a relation $\small{{\rho}}$ on G is a congruence if and only if there exists a normal subgroup N of G such that $\small{{\rho}=\{(s,\;t):st^{-1}{\in}N\}}$. 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 $\small{{\rho}=\{(s,\;t):st^{-1}{\in}N\}}$ on G is finitely presented.
Keywords
congruence;normal subgroup;semigroup presentation;
Language
English
Cited by
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