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A Jordan-Hölder Theorem for Finitary Groups
Published online by Cambridge University Press: 20 November 2018
Abstract
Let V be any left vector space over any division ring D and let G be any group of finitary linear maps of V. Then the D — G bimodule V satisfies a Jordan- Hölder theorem. Specifically, there is a bijection between the G-nontrivial factors in two composition series of V such that corresponding factors are isomorphic as D — G bimodules. This cannot be extended to cover the G-trivial factors.
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- Copyright © Canadian Mathematical Society 1995
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