Semigroup presentation for congruences on groups
Künye
Ayik, Gonca, Caliskan, Basri, (2013). Semigroup presentation for congruences on groups. Bulletin Of The Korean Mathematical Society. 50(2), 445-449. DOI: 10.4134/BKMS.2013.50.2.445Özet
We consider a congruence rho on a group G as a subsemigroup of the direct product G x 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) is an element of 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) is an element of N} on G is finitely presented.