Words periodic over the center of a division ring

Makar-Limanov, Leonid; Malcolmson, Peter

doi:10.1090/S0002-9939-1985-0776184-4

Words periodic over the center of a division ring
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by Leonid Makar-Limanov and Peter Malcolmson PDF

Proc. Amer. Math. Soc. 93 (1985), 590-592 Request permission

Abstract:

In generalization of a result of Herstein, the authors prove that, in a division ring with uncountable center, if any given nontrivial group word takes only values periodic over the center, then the division ring is commutative. Techniques include use of the result that a noncommutative division ring finite-dimensional over its center includes a nonabelian free group in its multiplicative group.

References

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