A rigidity theorem for group extensions
Let \(S\) denote the class of fundamental groups of closed surfaces of genus \(g\geq 2\). Denote by \(S^n\) the class of groups \(G\) admitting a filtration \(G=G_n\supset G_{n+1}\supset\cdots\supset G_1\supset G_0=\{1\}\), \(G_i\triangleleft G_{i+1}\), such that \(G_{i+1}/G_i\) lies in \(S\). One says that \(G\) possesses a poly-\(S\) structure if \(G\in S^n\) for some \(n\). The author proves that any group \(G\) possesses a poly-\(S\) structure.
scientific article; zbMATH DE number 1346249