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Subgroups of the basic subgroup in a modular group ring

Peter V. Danchev

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Rok, strany / Year, pages: 2005, 431-441

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Publikované / Published: 0000-00-00

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Suppose $R$ is an unitary commutative ring of prime characteristic $p$ and $G$ is an arbitrary abelian group with $p$-component $Gp$. The main results are that $S(RG)$ and $S(RG)/Gp$ are both starred groups, provided $Gp$ is not a divisible group. In the case when $Gp$ is divisible and $R$ is a perfect field, $S(RG)$ and $S(RG)/Gp$ are simply presented, whence a direct sum of a divisible group and a starred group. These claims enlarge statements argued by the author in Math. Bohem. (2004) and also give a new contribution to the old-standing Direct Factor Conjecture for group rings.

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