Artin's theorem on induced characters
In representation theory, a branch of mathematics, Artin's theorem, introduced by E. Artin, states that a character on a finite group is a rational linear combination of characters induced from cyclic subgroups of the group.
There is a similar but somehow more precise theorem due to Brauer, which says that the theorem remains true if "rational" and "cyclic subgroup" are replaced with "integer" and "elementary subgroup".
Proof
gollark: Oh no.
gollark: But there are something like 10 good ones.
gollark: Those don't actually need many crypto libraries. Why do people have 3000 of them?
gollark: Worryingly, the biggest category it defines is crypto libraries.
gollark: To be fair, some of these are probably specific to specific software.
References
- Serre, Jean-Pierre (1977-09-01). Linear Representations of Finite Groups. Graduate Texts in Mathematics, 42. New York–Heidelberg: Springer-Verlag. ISBN 978-0-387-90190-9. MR 0450380. Zbl 0355.20006.CS1 maint: ref=harv (link)
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