A NOTE ON GROUP IDENTITIES IN DIVISION RINGS

Author:

Chebotar M. A.,Lee P.-H.

Abstract

AbstractLet $D$ be a division ring whose group of units satisfies a non-trivial group identity $w$. Let $\alpha$ be the sum of positive degrees of indeterminates occurring in $w$. If the centre of $D$ contains more than $3\alpha$ elements, then $D$ is commutative.AMS 2000 Mathematics subject classification: Primary 16R50. Secondary 16K20

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Automorphism groups of vector spaces with generalized group identities;Linear and Multilinear Algebra;2021-06-10

2. *-Group identities on units of division rings;Communications in Algebra;2021-03-05

3. ON SOME SUBGROUPS OF D*WHICH SATISFY A GENERALIZED GROUP IDENTITY;Bulletin of the Korean Mathematical Society;2015-07-31

4. Existence of Nonabelian Free Subgroups in the Maximal Subgroups of GLn(D);Algebra Colloquium;2014-06-24

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