Every $G$-module is a submodule of a direct sum of cyclics
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- by Andy R. Magid PDF
- Proc. Amer. Math. Soc. 116 (1992), 929-937 Request permission
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).References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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