Algebras and Representation Theory

, Volume 9, Issue 3, pp 259–266 | Cite as

Modular Group Algebras with Almost Maximal Lie Nilpotency Indices

Article

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 \(|G^{\, \prime}|+1\), where \(|G^{\, \prime}|\) 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 \(|G^{\, \prime}|-p+2\).

Key words

group algebras Lie nilpotency indices dimensional subgroups 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Victor Bovdi
    • 1
    • 2
  • Tibor Juhász
    • 1
  • Ernesto Spinelli
    • 3
  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary
  2. 2.Institute of Mathematics and InformaticsCollege of NyíregyházaNyíregyházaHungary
  3. 3.Dipartimento di Matematica “E. De Giorgi”Università degli Studi di Lecce Via Provinciale Lecce-ArnesanoLecceItaly

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