Characters of Finite Abelian Groups
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چکیده
When G has size n and g ∈ G, for any character χ of G we have χ(g)n = χ(gn) = χ(1) = 1, so the values of χ lie among the nth roots of unity in S1. More precisely, the order of χ(g) divides the order of g (which divides #G). Characters on finite abelian groups were first studied in number theory, since number theory is a source of many interesting finite abelian groups. For instance, Dirichlet used characters on the group (Z/mZ)× to prove that when (a,m) = 1 there are infinitely many primes p ≡ a mod m. For a
منابع مشابه
Representation theory of finite abelian groups
Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/01 finite abelian.pdf] 1. Simultaneous eigenvectors for finite abelian groups 2. Cancellation lemma, orthogonality of distinct characters 3. Representations of finite abelian groups 4. Fourier expansions on finite abelian groups 5. Appendix: spectral theor...
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