Modular Group Algebras with Almost Maximal Lie Nilpotency Indices

Bódi, Viktor and Juhász, Tibor and Spinelli, Ernesto (2006) Modular Group Algebras with Almost Maximal Lie Nilpotency Indices. Algebras and Representation Theory, 9 (3). pp. 259-266. ISSN 1386-923X (print), 1572-9079 (online)

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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 ( and 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 authors previously determined those groups G for which this index is maximal and here they determine the groups G for which it is 'almost maximal', that is, it takes the next highest possible value, namely vertical bar G'vertical bar - p + 2.

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