Subgroups of the Klein bottle group and the mapping class of the Klein bottle. (English) Zbl 0673.57002

Summary: The isomorphism classes of subgroups of the fundamental group of the Klein bottle are determined algebraically and with a minimum of computation. Centralizers, radicals and maximal abelian subgroups, as well as a topological application, are also given. The mapping class group of the Klein bottle is then found in a purely algebraic fashion. The result is a by-product of the calculation of the group of automorphisms of the fundamental group of that surface, which is found in two different ways.


57M05 Fundamental group, presentations, free differential calculus