On group rings of abelian p-groups of any cardinality

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 n0 (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.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 381–392, October, 1969.