Basic subgroups in abelian group rings |
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Authors: | Peter V. Danchev |
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Affiliation: | (1) Faculty of Mathematics & Informatics, Dept. of Algebra, Paissii Hilendarski University of Plovdiv, 4000 Plovdiv, Bulgaria |
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Abstract: | Suppose is a commutative ring with identity of prime characteristic and is an arbitrary abelian -group. In the present paper, a basic subgroup and a lower basic subgroup of the -component and of the factor-group of the unit group in the modular group algebra are established, in the case when is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed -component and of the quotient group are given when is perfect and is arbitrary whose is -divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring is perfect and is -primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup. |
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Keywords: | basic and lower basic subgroups units modular abelian group rings |
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