All Questions
Tagged with conjugacy-classes finite-groups
7 questions
35
votes
2
answers
3k
views
Examples of finite groups with "good" bijection(s) between conjugacy classes and irreducible representations?
For symmetric group conjugacy classes and irreducible representation both are parametrized by Young diagramms, so there is a kind of "good" bijection between the two sets. For general finite groups ...
- 24.9k
8
votes
4
answers
2k
views
Product of conjugacy classes - is there an analog of Tanaka-Krein reconstruction ?
Consider a finite group G. The product of conjugacy classes can be defined in natural way just by multiplying the representatives and counting multiplicities (see e.g. MO 62088). So we get ring with ...
- 24.9k
9
votes
2
answers
860
views
What is natural about the well-known bijection between conjugacy classes and irreps of a symmetric group?
Symmetric groups possess a well-known bijection between conjugacy classes and irreducible representations. More precisely, both sets are indexed by Young diagrams.
Question: To what extent is this ...
- 24.9k
4
votes
1
answer
388
views
Number of conjugacy classes of pairs of commuting elements
Let $G$ be a finite group and denote by $r_G$ the number of conjugacy classes of pairs of commuting elements, i.e. the cardinality of the following set $$ A_G = \{ c(a_1,a_2) \ | \ a_1,a_2 \in G \text{...
12
votes
1
answer
602
views
Why would dim primitive irrep divide size of some conjugacy class ?
From Isaacs et.al. 2005
Conjecture C. Let χ be a primitive
irreducible character of an arbitrary
finite group G. Then χ(1) divides |
clG(g)| for some element g ∈ G.
Here, of course, we ...
- 24.9k
7
votes
1
answer
356
views
Number of conjugacy classes of pairs of commuting elements II
This post follows up on a discussion initiated in Number of conjugacy classes of pairs of commuting elements.
Consider a finite group $G$ and let $r_G$ represent the number of conjugacy classes of ...
3
votes
2
answers
738
views
Rational Conjugacy Classes of Finite Groups
Suppose $G$ is a finite group and $A$ is the set of all character values of $G$. By character values, I mean entries of the character table of $G$. Let $\Gamma = \operatorname{Gal}({\mathbb{Q}(A)}/{\...
