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

Magid, Andy R.

doi:10.1090/S0002-9939-1992-1100660-1

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).

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