Caractéristiques d'Euler et groupes fondamentaux des variétés de dimension 4
Using a simple argument based on the multiplicative behaviour of the Euler characteristic with respect to a finite covering it is shown that if a 2-knot group has finite commutator subgroup T, then every abelian subgroup of T is cyclic (Theorem 5) and that there are finitely presentable superperfect groups which are not the fundamental groups of 4-dimensional homology spheres. (A result close to Theorem 5 was obtained by the reviewer [Bull. Aust. Math. Soc. 16, 449-462 (1977; Zbl 0352.57011)]. With regard to the closing problem of the article under review, it should be noted that \textit{C. M. Campbell} and \textit{E. F. Robertson} [Bull. Lond. Math. Soc. 12, 17-20 (1980; Zbl 0393.20020)] have shown that if p is a prime \(\geq 5\), then the finite group SL(2,p) has a presentation of deficiency 0; as it is superperfect it is the group of an homology 4-sphere.)
finitely presentable superperfect groups
fundamental groups of 4-dimensional homology spheres
scientific article; zbMATH DE number 3903568