Evolving groups

Article
  • 20 Downloads

Abstract

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.

Keywords

Cohomology Tate groups Finite groups Evolving groups Intense automorphisms 

Mathematics Subject Classification

12G05 20D20 20E34 20F16 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Berhuy, An Introduction to Galois Cohomology and its Applications, London Mathematical Society Lecture Notes Series, 377, Cambridge University Press, Cambridge, 2010.CrossRefGoogle Scholar
  2. 2.
    J.W.S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, London, 1967.MATHGoogle Scholar
  3. 3.
    P. Gille and T. Szamuely, Central Simple Algebras and Galois Cohomology, Cambridge Studies in Advanced Mathematics, 101, Cambridge University Press, Cambridge, 2006.CrossRefMATHGoogle Scholar
  4. 4.
    M. Isaacs, Finite Group Theory, Graduate Studies in Mathematics, 92, American Mathematical Society, Providence, RI, 2008.Google Scholar
  5. 5.
    S. Lang and J. Tate, Principal homogeneous spaces over abelian varieties, Amer. J. Math. 80 (1958), 659–684.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    M. Stanojkovski, Evolving groups, Master’s thesis, Retrieved from https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/stanojkovskimaster.pdf, Leiden, 2013.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

Personalised recommendations