Geodesic
Browder--Livesay groups for Abelian 2-groups
Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 499-540

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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. 
@article{SM_1991_70_2_a10,
     author = {Yu. V. Muranov and A. F. Kharshiladze},
     title = {Browder--Livesay groups for {Abelian} 2-groups},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_2_a10/}
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Yu. V. Muranov; A. F. Kharshiladze. Browder--Livesay groups for Abelian 2-groups. Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 499-540. http://geodesic.mathdoc.fr/item/SM_1991_70_2_a10/