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Results tagged with finite-groups
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user 65
Questions on group theory which concern finite groups.
12
votes
4
answers
2k
views
Mystery of the Monstrous Moonshine
There's a very famous group, the largest sporadic simple finite group, sometimes called a monster whose size is quoted below. What's the explanation that the primes appearing in it,
#{Monster} = 2 …
- 15.1k
12
votes
Number of irreducible representations
It's not entirely trivial, but here's the sketch of the proof if you would like to finish it yourself. Note that people usually denote complex numbers by $\mathbb C$:
(1) Every irreducible represe …
- 15.1k
5
votes
Number of faithful representations of a finite group
I haven't heard this question before, but I would approach it in a following way: you know some basic relations between irreducible representations of a groups — e.g. their # is the # of conjugacy cl …
- 15.1k
-3
votes
Why are characters so well-behaved?
There are lots of good points in other answers, so I want to to add one specific thing about why representations are uniquely defined by their characters.
Irreducible representations are uniquely det …
- 15.1k