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The Quarterly Journal of Mathematics Advance Access originally published online on May 15, 2007
The Quarterly Journal of Mathematics 2007 58(2):229-247; doi:10.1093/qmath/ham012
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

CHARACTERISTIC NILPOTENT SUBGROUPS OF BOUNDED CO-RANK AND AUTOMORPHICALLY INVARIANT NILPOTENT IDEALS OF BOUNDED CODIMENSION IN LIE ALGEBRAS

E. I. Khukhro1,{dagger} and N. YU. Makarenko {ddagger}2

1 School of Mathematics, Cardiff University, Cardiff, CF23 9ED, U.K
2 Sobolev Institute of Mathematics, SO RAN, Novosibirsk-90, 630 090, Russia

{dagger} Corresponding author. E-mail: khukhro{at}cardiff.ac.uk

Received 3 November 2006; revised 25 January 2007
  Abstract

It is proved that if a Lie algebra L has a nilpotent ideal of nilpotency class c and of finite codimension r, then L has also a nilpotent ideal of class ≤ c and of finite codimension bounded in terms of r and c that is invariant under all automorphisms of L. In a similar result for groups, the role of dimension is played by rank: if a group G has a normal nilpotent subgroup H of class c such that the quotient group G/H has finite rank r and H is either torsion-free or periodic, then G has also a characteristic nilpotent subgroup C of class ≤ c with quotient G/C of finite rank bounded in terms of r and c.

{ddagger} E-mail: natalia_makarenko{at}yahoo.fr


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