On Lie nilpotent modular group algebras

ABSTRACT

Let K be a field of characteristic p>0 and let KG be the group algebra of an arbitrary group G over K. It is known that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least p+1. The group algebras KG for which these indices are p+1 or 2p or 3p−1 or 4p−2 have already been determined. In this paper, we classify the group algebras KG for which the upper Lie nilpotency index is 5p−3, 6p−4 or 7p−5.

KEYWORDS:

• Group algebras
• Lie dimension subgroups
• Lie nilpotency index

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16S34
• Secondary 17B30