On Lie nilpotent modular group algebras.

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