We know that for a (finite-dimensional) vector space over some fixed field $k$, we may construct its dual as the set of all its linear functionals. Now for a given (finite) group $G$, we may construct its set of all Dirichlet characters $\hat{G}$ and $\hat{G}$ forms a group. Now, does $\hat{G}$ act as some sort of a dual of $G$, similar of some sort to the dual construction of a vector space? Also, what information do $\hat{G}$ tell about $G$? Are they isomorphic if $G$ is finite as in the case of finite-dimensional vector spaces? Thanks.
2026-03-24 20:33:28.1774384408
Is the character group of a finite group its "dual"?
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