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The paper constructs an `exotic' algebraic 2-complex over the generalizedquaternion group of order 28, with the boundary maps given by explicit matricesover the group ring. This result depends on showing that a certain ideal of thegroup ring is stably free but not free. As it is not known whether the complexconstructed here is geometrically realizable, this example is proposed as asuitable test object in the investigation of an open problem of C.T.C. Wall,now referred to as the D(2)-problem.

A stably free nonfree module and its relevance for homotopy classification, caseQ28

A stably free nonfree module and its relevance for homotopy classification, caseQ₂₈