Article contents
On the Semisimplicity of Modular Group Algebras. II
Published online by Cambridge University Press: 20 November 2018
Extract
Let G be a discrete group, let Kbe an algebraically closed field of characteristic p > 0 and let KGdenote the group algebra of Gover K.In a previous paper (2) I studied the Jacobson radical JKGof KGfor groups Gwith big abelian subgroups or quotient groups. It is therefore natural to next consider metabelian groups, and I do this here. The main result is as follows.
THEOREM 1. Let K be an algebraically closed field of characteristic p and let a group G have a normal abelian subgroup A with G/A abelian. Then JKG ≠ {0} if and only if G has an element g of order p such that the A-conjugacy class gA is finite and such that the group is periodic.
Note that since and G/Ais abelian, we do in fact have
.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1969
References
- 3
- Cited by