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Modular Group Algebras with Almost Maximal Lie Nilpotency Indices

Authors:	Victor Bovdi Tibor Juhász Ernesto Spinelli

Affiliation:	(1) Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary;(2) Institute of Mathematics and Informatics, College of Nyíregyháza, Sóstói út 31/b, H-4410 Nyíregyháza, Hungary;(3) Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy

Abstract:	Let be a field of positive characteristic and the group algebra of a group . It is known that, if is Lie nilpotent, then its upper (and lower) Lie nilpotency index is at most $\|G^{, prime}\|+1$ , where $\|G^{, prime}\|$ is the order of the commutator subgroup. The authors previously determined those groups for which this index is maximal and here they determine the groups for which it is `almost maximal', that is, it takes the next highest possible value, namely $\|G^{, prime}\|-p+2$ .Presented by V. Dl a b.Dedicated to Professor Vjacheslav Rudko on his 65th birthday.The research was supported by OTKA No. T 037202, No. T 038059 and Italian National Research Project “Group Theory and Application.”

Keywords:	group algebras Lie nilpotency indices dimensional subgroups
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