Subgroups of finitely presented groups

@article{Higman1961SubgroupsOF,
  title={Subgroups of finitely presented groups},
  author={Graham Higman},
  journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
  year={1961},
  volume={262},
  pages={455 - 475}
}
  • G. Higman
  • Published 8 August 1961
  • Mathematics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It follows that every countable A belian group, and every countable locally finite group can be so embedded; and that there exists a finitely presented group which simultaneously embeds all finitely presented groups. A nother corollary of the theorem is the known fact that there exist finitely presented… 
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References

Computability and Unsolvability
  • Martin D. Davis
  • Computer Science
    McGraw-Hill Series in Information Processing and Computers
  • 1958
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