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 ${\rho} Keywords congruence;normal subgroup;semigroup presentation; Language English Cited by References 1. I. M. Araujo, M. J. J. Branco, V. H. Fernandes, G. M. S. Gomes, and N. Ruskuc, On generators and relations for unions of semigroups, Semigroup Forum 63 (2001), no. 1, 49-62. 2. H. Ayik and N. Ruskuc, Generators and relations of Rees matrix semigroups, Proc. Edinburgh Math. Soc. (2) 42 (1999), no. 3, 482-495. 3. G. Ayik, H. Ayik, and Y. Unlu, Presentations for S and$S/{\rho}$from a given presentation${\rho}\$, Semigroup Forum 70 (2005), no. 1, 146-149.

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