In: Mathematica Slovaca, vol. 55, no. 4
Peter V. Danchev
Subgroups of the basic subgroup in a modular group ring
Year, pages: 2005, 431 - 441
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.
How to cite:
Danchev, P. 2005. Subgroups of the basic subgroup in a modular group ring. In Mathematica Slovaca, vol. 55, no.4, pp. 431-441. 0139-9918.
Danchev, P. (2005). Subgroups of the basic subgroup in a modular group ring. Mathematica Slovaca, 55(4), 431-441. 0139-9918.