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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S. D. Berman, “Group algebras of countable Abelian p-groups,” Publ. Math.,14, Nos. 1–4, 365–405 (1967).
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P. Grawley, “Abelian p-groups determined by their Ulm sequences,” Pacific J. Math.,22, No. 2, 235–239 (1967).
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Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 381–392, October, 1969.
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Berman, S.D., Mollov, T.Z. On group rings of abelian p-groups of any cardinality. Mathematical Notes of the Academy of Sciences of the USSR 6, 686–692 (1969). https://doi.org/10.1007/BF01093802
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DOI: https://doi.org/10.1007/BF01093802