The derived group of a permutation representation
The author describes an algebraic construction which unifies in a single theory the basic algebra associated with knot groups, Alexander matrices, and covering spaces. The construction is modelled on the algebra of liftings of closed paths in a base space B to paths in a covering space E of B. The object constructed is a group A. The author proves a structure theorem for this group which, in the model case, exhibits the group as the free product of \(\pi_ 1(E)\) with a free group. The author uses the construction to give an elegant formulation of the Reidemeister-Schreier algorithm for finding a presentation of a subgroup of a presented group.
scientific article; zbMATH DE number 3872279