Charasteristic nilpotent subgroups of bounded co-rank and automorphically invariant nilpotent ideals of bounded codimension in lie algebras

• Autores: E. I. Khukhro, N. Y. Makarenko
• Localización: Quarterly journal of mathematics, ISSN 0033-5606, Vol. 58, Nº. 2, 2007, págs. 229-247
• Idioma: inglés
• DOI: 10.1093/qmath/ham012
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• Resumen

  • 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.