  We develop a theory of `non-abelian higher special elements' in the
non-commutative exterior powers of the Galois cohomology of $p$-adic
representations. We explore their relation to the theory of organising matrices
and thus to the Galois module structure of Selmer modules. In concrete
applications, we relate our general theory to the formulation of refined
conjectures of Birch and Swinnerton-Dyer type and to the Galois structure of
Tate-Shafarevich and Selmer groups of abelian varieties.
