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: I don't have those. I just do computers. Besides, bioweapons could affect other people.
gollark: I would recommend against entering the field of bioweapon design.
gollark: I'm pretty sure lots of viruses cover themselves (partly) in marker proteins from human cells, so it's harder to deal with them.
gollark: If you could do that conveniently, we would probably already have evolved this capability.
gollark: They said an RNA vaccine. Anyone can make RNA. Maybe not the magic lipid things.
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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