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Every $ G$-module is a submodule of a direct sum of cyclics


Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 116 (1992), 929-937
MSC: Primary 20C07; Secondary 20G05
DOI: https://doi.org/10.1090/S0002-9939-1992-1100660-1
MathSciNet review: 1100660
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Abstract: Let $ G$ be a group and $ V$ a finite-dimensional complex $ G$-module. It is shown that $ G$ is (isomorphic to) a submodule of a direct sum $ {W_1} \oplus \cdots \oplus {W_S}$ where each $ {W_i}$ is a cyclic finite-dimensional complex $ G$-module. If $ G$ is an analytic (respectively algebraic) group and $ V$ is an analytic (respectively rational) module then the $ {W_i}$ can be taken to be analytic (respectively rational).


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1100660-1
Keywords: Algebraic group, rational module
Article copyright: © Copyright 1992 American Mathematical Society

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