Isomorphism Characterization of Divisible Groups in Modular Abelian Group Rings
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Abstract Suppose G is an abelian group with a p-subgroup H and R is a commutative unitary ring of prime characteristic p with trivial nil-radical. We give a complete description up to isomorphism of the maximal divisible subgroups of 1 + I(RG;H) and (1 + I(RG;H))=H, respectively, where I(RG;H) denotes the relative augmentation ideal of the group algebra RG with respect to H. This paper terminates a series of works by the author on the topic, first of which are [Danchev, Rad. Mat. 13: 23–32, 2004] and [Danchev, Bull. Georgian Acad. Sci. 174: 238–242, 2006].
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1979 ◽
Vol 85
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pp. 247-252
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1977 ◽
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pp. 365-368
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2018 ◽
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pp. 2050021
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1992 ◽
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pp. 503-506
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2010 ◽
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pp. 93-102
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2016 ◽
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pp. 1650150
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2017 ◽
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pp. 1750200
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