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Bulletin of the London Mathematical Society 1994 26(5):431-437; doi:10.1112/blms/26.5.431
© 1994 by London Mathematical Society
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© London Mathematical Society

The Coclass of a Restricted Lie Algebra

D. M. Riley and J. F. Semple

Mathematical Institute University of Oxford 24–29 St Giles' Oxford OX1 3LB

Received 17 August 1992. Revision received 30 June 1993.

Let L be a finite dimensional nilpotent Lie algebra. Denote the dimension and nilpotence class of L by dim(L) and cl(L), respectively. The coclass of L is defined to be cc(L) = dim(L) –cl(L). We prove that if L is a restricted Lie algebra over a field of characteristic p, then dim(L) is bounded by a certain function of p and cc(L) only. This is an analogue of the coclass conjectures for p-groups. We deduce a ‘Lie-coclass’ result for p-groups.

Current address,Department of Mathematics University of Alabama Tuscaloosa, AL 35487-0350 USA


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