Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SEMIGROUP PRESENTATIONS FOR CONGRUENCES ON GROUPS

  • Ayik, Gonca (Department of Mathematics Cukurova University) ;
  • Caliskan, Basri (Department of Mathematics Osmaniye Korkut Ata University)
  • Received : 2011.09.22
  • Published : 2013.03.31
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Abstract

We consider a congruence ${\rho}$ on a group G as a subsemigroup of the direct product $G{\times}G$. 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 ${\rho}=\{(s,\;t):st^{-1}{\in}N\}$. 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 ${\rho}=\{(s,\;t):st^{-1}{\in}N\}$ on G is finitely presented.

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References

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