Abstract
Suppose F is a perfect field of characteristic p ≠ 0 and G is a multiplicatively written abelian p-group. Write bpd( H) for the balanced-projective dimension of an arbitrary p-group H. If V( G) is the group of normalized units of the group algebra F( G), it is shown that bpd( V( G)) = bpd( G). This was known previously only in the special case where one of the dimensions is zero. Also, some partial results are obtained concerning the conjecture that the functor G↦ V(G) G decreases balanced-projective dimension. Special cases of these results are related to the unresolved direct factor problem: When is G a direct factor of the group of units of F( G)?
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