Whitehead torsion V (Ex)
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Exercise 0.1.
- Show that the operations (1)-(5) from [Lück2001, Section 1.4] used in the definition of the Whitehead group in fact yield equivalence classes of invertible matrices of arbitrary size.
- Show that addition is well-defined in the Whitehead group via
Here and are invertible matricies over the group ring , is an matrix, is an matrix with , denotes the zero and matricies and denotes matrix multiplication.
- Show that is trivial.