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2 results

  • ANOSOV DIFFEOMORPHISMS ON A CLASS OF 2-STEP NILMANIFOLDS

  • KAREL DEKIMPE, SANDRA DESCHAMPS
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 2 / May 2003
    Published online by Cambridge University Press:
    31 July 2003, pp. 269-280
    Print publication:
    May 2003
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  • In this paper we study nilmanifolds which are modeled on a quotient of a free 2-step nilpotent Lie group by a 1-dimensional subgroup. In fact we obtain a very easy criterion to decide whether or not such a nilmanifold admits an Anosov diffeomorphism.

  • On groups in which every subgroup is subnormal of defect at most three

  • Part of
  • Gunnar Traustason
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 64 / Issue 3 / June 1998
    Published online by Cambridge University Press:
    09 April 2009, pp. 397-420
    Print publication:
    June 1998
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  • In this paper we study groups in which every subgroup is subnormal of defect at most 3. Let G be a group which is either torsion-free or of prime exponent different from 7. We show that every subgroup in G is subnormal of defect at most 3 if and only if G is nilpotent of class at most 3. When G is of exponent 7 the situation is different. While every group of exponent 7, in which every subgroup is subnormal of defect at most 3, is nilpotent of class at most 4, there are examples of such groups with class exactly 4. We also investigate the structure of these groups.