Modular group algebras with almost maximal Lie nilpotency indices, II

Details Modular group algebras with almost maximal Lie nilpotency indices, II Modular group algebras with almost maximal Lie nilpotency indices, II

2006-07-06

arxiv.org/abs/math/0607152v1

Mathematics

Rings and Algebras

7 pages

Scientific paper

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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