Geodesic
Basic subgroups in abelian group rings
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 129-140.

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Suppose $R$ is a commutative ring with identity of prime characteristic $p$ and $G$ is an arbitrary abelian $p$-group. In the present paper, a basic subgroup and a lower basic subgroup of the $p$-component $U_p(RG)$ and of the factor-group $U_p(RG)/G$ of the unit group $U(RG)$ in the modular group algebra $RG$ are established, in the case when $R$ is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed $p$-component $S(RG)$ and of the quotient group $S(RG)/G_p$ are given when $R$ is perfect and $G$ is arbitrary whose $G/G_p$ is $p$-divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring $R$ is perfect and $G$ is $p$-primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup.
Classification : 16U60, 20C07, 20K10
Keywords: basic and lower basic subgroups; units; modular abelian group rings 
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     author = {Danchev, Peter V.},
     title = {Basic subgroups in abelian group rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {129--140},
     publisher = {mathdoc},
     volume = {52},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002__52_1_a11/}
}
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Danchev, Peter V. Basic subgroups in abelian group rings. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 129-140. http://geodesic.mathdoc.fr/item/CMJ_2002__52_1_a11/