134 research outputs found
Normality in group rings
Let be the group ring of a group over a commutative ring with
unity. The rings are described for which for all
, where \quad \quad is an involution of ; here is
a homomorphism and is an anti-automorphism of order two of .Comment: 8 page
Modular group algebras with almost maximal Lie nilpotency indices. I
Let K be a field of positive characteristic p and KG the group algebra of a
group G. It is known that, if KG is Lie nilpotent, then its upper (or lower)
Lie nilpotency index is at most |G'|+1, where |G'| is the order of the
commutator subgroup. The authors have previously determined the groups G for
which this index is maximal and here they determine the G for which it is
`almost maximal', that is the next highest possible value, namely |G'|-p+2
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