#### Z. Reichstein, B. Youssin, *
Splitting fields of G-varieties *, Pacific J. Math.,
200 (2001), 207-249.

** Abstract: **
Let G be an algebraic group, X a generically free G-variety, and K=k(X)^G.
A field extension L of K is called a splitting field of X if the image
of the class of X under the natural
map H^1(K, G) ---> H^1(L, G) is trivial.
If L/K is a (finite) Galois extension then Gal(L/K) is called
a splitting group of X.
We prove a lower bound on the size of a splitting field of X in terms
of fixed points of nontoral abelian subgroups of G. A similar result
holds for splitting groups. We give a number of applications, including
a new construction of noncrossed product division algebras.

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