Browder–Livesay groups for Abelian 2-groups

The authors compute all the Browder–Livesay groups of an arbitrary finite abelian 2-group with an arbitrary orientation character and any subgroup of index 2. Browder–Livesay groups are obstruction groups for the problem of splitting homotopy equivalences of manifolds along one-sided submanifolds of codimension 1. All the connections with the Wall groups of abelian 2-groups which can be expressed by two-row diagrams are uncovered.