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# Cartan–Brauer–Hua theorem

In abstract algebra, the **Cartan–Brauer–Hua theorem** (named after Richard Brauer, Élie Cartan, and Hua Luogeng) is a theorem pertaining to division rings. It says that given two division rings *K* ⊆ *D* such that *xKx*^{−1} is contained in *K* for every *x* not equal to 0 in *D*, either *K* is contained in the center of *D*, or *K* = *D*. In other words, if the unit group of *K* is a normal subgroup of the unit group of *D*, then either *K* = *D* or *K* is central (Lam 2001, p. 211).

References

Herstein, I. N. (1975). Topics in algebra. New York: Wiley. p. 368. ISBN 0-471-01090-1.

Lam, Tsit-Yuen (2001). A First Course in Noncommutative Rings (2nd ed.). Berlin, New York: Springer-Verlag. ISBN 978-0-387-95325-0. MR 1838439.

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