The embedding of certain linear and Abelian groups in finitely presented simple groups
This paper continues the previous one [reviewed above] and applies the results there to embed some groups in finitely presented simple groups. \textit{G. Higman} [in ''Finitely presented simple groups'', Notes on Pure Mathematics 8, The Australian National University Canberra (1974)], showed that any countable locally finite group can be embedded in a finitely presented simple group. The author extends this to show that any linear group over the integers and any countable abelian group where the quotient by the torsion subgroup is a subgroup of a free Z[1/n]-module for some integer n, can be embedded in a finitely presented simple group. This gives some new results, for GL(3,Z) could not be embedded in any of the previously known finitely presented simple groups. The methods used are very similar to those of the previous paper and this should be read in conjunction with that paper.
scientific article; zbMATH DE number 3865566