• DOI:10.1098/rspa.1961.0132
• Corpus ID: 120100270

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 groups with recursively insoluble word problem . A by-product of the proof is a genetic characterization of the recursively enumerable subsets of a suitable effectively enumerable set.