Lie nilpotency indices of modular group algebras

Bódi, Viktor and Srivastava, J. B. (2010) Lie nilpotency indices of modular group algebras. ALGEBRA COLLOQUIUM, 17 (1). pp. 17-26. ISSN 1005-3867

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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 tipper (or lower) Lie nilpotency index is at most vertical bar G'vertical bar +1, where vertical bar G'vertical bar is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal has already been determined. Here we determine G for which tipper (or lower) Lie nilpotency index is the next highest possible.

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