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Modular group algebras with almost maximal Lie nilpotency indices. I

Victor Bovdi·Tibor Juhasz·Ernesto Spinelli
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Abstract

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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Victor Bovdi, Tibor Juhasz, Ernesto Spinelli. 2005-07-13. Modular group algebras with almost maximal Lie nilpotency indices. I. https://arxiv.org/abs/math/0507261

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