A dihedral calculus for groups (Q1108381)

A method is described for calculating dihedral quotients of a group given by a presentation in much the same spirit as the usual calculation of abelian quotients. The term dihedral is used in a generalized sense to mean any group which is an extension of an abelian group by the inverting automorphism; it is a free dihedral group if the abelian subgroup is free. Ways of investigating free dihedral quotients of free groups and hence of arbitrary groups are described. Some applications are also given. For example, it is shown that a group with deficiency at least 2 must have at least 3 distinct infinite dihedral quotients.