Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.


i wonder if there is a simple argument to show that no group of order 48 can have an irreducible character of degree larger than 4?

Thanks, Karim

share|cite|improve this question

closed as off topic by Qiaochu Yuan, Andrés Caicedo, Mark Sapir, Chris Godsil, Alex Bartel May 22 '12 at 0:04

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

Edited to change 6 to 4 per karim's clarification. – Will Sawin May 21 '12 at 21:26
I wonder whether it's an interesting question to ask for groups of order $n$ with an irreducible character of degree $d$ with $(d+1)^2\ge n$? The group $A_4$, of order 12, has an irreducible character of degree 3; there's a group of order 20 with an irrep of degree 4, and a group of order 42 with an irrep of degree 6. – Gerry Myerson May 21 '12 at 23:25
@Mark is right. Why bother asking questions about any group of order less than 2000? – Steve D May 21 '12 at 23:34
@Gerry: They have been known for a while. See – S. Carnahan May 22 '12 at 0:05
@Steve D: I am not sure you understand what you are saying. There are 4725 groups of order 864, for example, and you need a CAS to treat them. There are only 52 groups of order 48, and you can treat them by hand. Each one of them has a normal subgroup of order 16 or 8. In the first case, it is an extension of a group of order 16 by a group of order 3, in the second case it is an extension of a group of order 8 by $S_3$. Also not every question about a small group is trivial. For example, construct a hyperbolic 6-manifold with isometry group $S_3$, if you can (hint: it can be done). – Mark Sapir May 22 '12 at 0:18

Browse other questions tagged or ask your own question.