SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS


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AYIK G. , Caliskan B.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.50, ss.445-449, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 50 Konu: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.4134/bkms.2013.50.2.445
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.445-449

Özet

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.