Abstract
SupposeP is the ring ofp-adic integers,G is a finite group of orderpn, andPG is the group ring ofG overP. IfVp(G) denotes the elements ofPG with coefficient sum one which are of order a power ofp, it is shown that the elements of any subgroupH ofVp(G) are linearly independent overP, and if in additionH is of orderpn, thenPG≅PH. As a consequence, the lattice of normal subgroups ofG and the abelianization of the normal subgroups ofG are determined byPG.
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