SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS

Gonca Ayik, Basri Caliskan
2013 Bulletin of the Korean Mathematical Society  
We consider a congruence ρ on a group G as a subsemigroup of the direct product G × G. It is well known that a relation ρ on G is a congruence if and only if there exists a normal subgroup N of G such that ρ = (s, t) : st −1 ∈ 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 ρ = (s, t) : st −1 ∈ N on G is finitely presented.
doi:10.4134/bkms.2013.50.2.445 fatcat:zfcabup5zzhljli34e4l2zwkq4