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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Solvable subgroups in prime rings

Author: Charles Lanski
Journal: Proc. Amer. Math. Soc. 82 (1981), 533-537
MSC: Primary 16A25
MathSciNet review: 614873
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Abstract: Let $ R $ be a prime ring with center $ Z$ and group of units $ U$. The main theorem shows that any solvable normal subgroups of $ U$ must lie in $ Z$, provided that $ R$ is not a domain, $ Z$ is large enough, and that the $ Z$-subalgebra generated by $ U$ contains a nonzero ideal of $ R$. One consequence is the determination of the structure of $ R$ when $ R$ has an involution and the subgroup of $ U$ generated by the symmetric units is solvable.

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PII: S 0002-9939(1981)0614873-9
Article copyright: © Copyright 1981 American Mathematical Society