Skip to main content
Log in

Unitary groups as stabilizers of orbits

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

We show that a finite unitary group which has orbits spanning the whole space is necessarily the setwise stabilizer of a certain orbit.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. M. Isaacs, Linear groups as stabilizers of sets, Proc. Amer. Math. Soc. 62 (1977), 28–30.

    Article  MathSciNet  MATH  Google Scholar 

  2. L. Babai, Symmetry groups of vertex-transitive polytopes, Geometriae Dedicata 6 (1977), 331–337.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Friese and F. Ladisch, Classification of affine symmetry groups of orbit polytopes, Preprint (2016), available at arXiv:1608.06539.

  4. D. S. Dummit and R. M. Foote, Abstract Algebra, Third edition, John Wiley & Sons, Inc., Hoboken, NJ, 2004.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erik Friese.

Additional information

The author is partially supported by DFG-grant SCHU 1503/6-1.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Friese, E. Unitary groups as stabilizers of orbits. Arch. Math. 109, 101–103 (2017). https://doi.org/10.1007/s00013-017-1065-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-017-1065-9

Keywords

Mathematics Subject Classification

Navigation