SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS


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AYIK G. , Caliskan B.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.50, no.2, pp.445-449, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.4134/bkms.2013.50.2.445
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.445-449

Abstract

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.