Modular group algebras with almost maximal Lie nilpotency indices II.

Bódi, Viktor (2007) Modular group algebras with almost maximal Lie nilpotency indices II. Mathematica Japonica, 65 (2). pp. 267-271. ISSN 0025-5513

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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. Previously we determined the groups G for which the upper/lower nilpotency index is maximal or the upper nilpotency index is ‘almost maximal’ (that is, of the next highest possible value, namely |G'�| − p + 2). Here we determine the groups for which the lower nilpotency index is ‘almost maximal’.

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