Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 1 down vote favorite
1

For a finite group $G$, there are structure constants related to the group such as number of Sylow-p subgroups, orders of conjugacy classes. What are other constants related to the group?

share|improve this question
8  
I suggest reading a book on group theory and one on character theory. Your question is about as broad as "what other words are there in the English language apart from 'car' and 'yesterday'". – Alex B. Apr 6 '11 at 3:57
Why do you ask this? @Phillip – awllower Apr 6 '11 at 3:58
2  
Waaaaaay too many to list (orders of elements; multiset of orders of elements; degrees of irreducible representations; orders of verbal/marginal subgroups). This is too vague to be a real question; voting to close. – Arturo Magidin Apr 6 '11 at 4:04
@allower: I am doing various computations for small groups; so I was thinking that if some data related to structure constants is available, then the problems will be easy to solve. – user8186 Apr 6 '11 at 4:05
Are you trying to distinguish between groups through a finite set of numerical invariants? You're not going to be able to. For example, there is no known finite set of numerical invariants that can distinguish finite $p$-groups up to isomorphism; and it is widely believed no such set can exist. – Arturo Magidin Apr 6 '11 at 4:10

closed as not a real question by Arturo Magidin, Ross Millikan, Akhil Mathew Apr 6 '11 at 4:52

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.