Finitely generated groups L with \(L\approx L\times M\), \(M\neq 1\), M finitely presented (Q1078667)

Examples of non-trivial finitely generated groups isomorphic to a proper direct factor of themselves have long been known [\textit{J. M. Tyrer Jones}, J. Aust. Math. Soc. 17, 174-196 (1974; Zbl 0286.20040)]. The author shows that this can be done with the complementary factor finitely presented, and promises in a note added in proof that in a future publication it will be shown that the whole group itself, as well as the complementary factor, can be chosen finitely presented. \{The reviewer animadverts upon the use of mathematical symbols in titles of papers: they lead to difficulties in indexing, referencing, reviewing. The list of references is inaccurate, because the author mostly, but not consistently, omits middle initials; thus the author of the paper quoted above becomes just ''J. Jones'', and the well-known book by Wilhelm Magnus, Abraham Karrass, and Donald Solitar is ascribed to ''K. Magnus, Solitar''.\}