Matrix Groups pp 106-123 | Cite as

Covering by Maximal Tori

  • Morton L. Curtis
Part of the Universitext book series (UTX)


In Exercise 4 of Chapter VII one showed that if T is a maximal torus in a matrix group G, then for any x ∈ G, xTx−1 is also a maximal torus. What we prove in this chapter is that if T is our standard maximal torus in one of our connected matrix groups G, then
$$ {\text{G}}\;{\text{ = }}\;\mathop {\text{U}}\limits_{{\text{x}} \in \;{\text{G}}} \;{\text{xT}}{{\text{x}}^{{\text{ - 1}}}} $$
showing that every element of G lies in at least one maximal torus.


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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Morton L. Curtis
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA

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