Kulikov, V. S. Alexander modules of irreducible \(C\)-groups. (English. Russian original) Zbl 1144.14022 Izv. Math. 72, No. 2, 305-344 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 2, 105-150 (2008). The author gives an algebraic characterization of the Alexander modules of knotted \(n\)-manifolds in the sphere \(S^{n+2}\), \(n \geq 2\), and of the Alexander modules of irreducible Hurwitz curves. For instance, it is shown that a finitely generated abelian group \(G\) is the Alexander module of some irreducible Hurwitz curve if and only if there is a positive integer \(m\) and an automorphism \(h\) of \(G\) such that \(h^m=Id\) and \(h-Id\) is also an automorphism of \(G\). It would be interesting to decide when such a group \(G\) is the Alexander module of some irreducible algebraic plane curve. Reviewer: Alexandru Dimca (Nice) MSC: 14H30 Coverings of curves, fundamental group 57M05 Fundamental group, presentations, free differential calculus 57R17 Symplectic and contact topology in high or arbitrary dimension Keywords:knotted manifolds; Hurwitz curves; Alexander modules PDFBibTeX XMLCite \textit{V. S. Kulikov}, Izv. Math. 72, No. 2, 305--344 (2008; Zbl 1144.14022); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 2, 105--150 (2008) Full Text: DOI arXiv