Abstract
The problem is studied of the connection between an Abelian p-group G of arbitrary cardinality and its group ring LG, where L is a ring with unity nonzero characteristic n≡0 (mod p), with p being a prime. In particular, it is shown that group ring LG defines to within isomorphism the basis subgroup of group G. If reduced Abelian p-group G has finite type and if its Ulm factors decompose into direct products of cyclic groups, then group ring LG determines group G to within isomorphism.
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