Definition:G-Submodule

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Definition

Let $\struct {G, \cdot}$ be a finite group.

Let $\struct {V, \phi}$ be a $G$-module.

Let $W$ be a vector subspace of $V$.


Let $\phi$ be a linear group action when restricted to $G \times W \subseteq G \times V$.

Let $\phi_W$ be the restriction of $\phi$ to $G \times W$.


Then $\struct {W, \phi_W}$ is called a $G$-submodule of $\struct {V, \phi}$.


Also see


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