Applications of Representations and Butler Groups
The theory of Butler groups has, a priori, little relevance for p-local torsion-free groups. This is so because p-local Butler groups are completely decomposable. Nevertheless, isomorphism at p classes of finite rank Butler groups can be interpreted as torsion-free ℤ p -modules of finite rank (Corollary 8.1.9). Rank-1 groups correspond to purely indecomposable p-local groups, and bracket groups correspond to copurely indecomposable p-local groups.
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