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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\®■ -®WS where each W¡ 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¡ can be taken to be analytic (respectively rational).

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