The conjugacy-classes tag has no wiki summary.
1
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2answers
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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 = ...
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2answers
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existence of a finite group which is the union of self normalizing subgroups
Can a finite group G be the union of self normalizing subgroups such that the intersection between any two of these subgroups is equal to the unit of the group G? I don't think so but I can't prove ...
5
votes
2answers
380 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 ...
9
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1answer
326 views
The Simultaneous Conjugacy Problem in the symmetric group $S_N$
We are interested in the following notions in the case $G=S_N$, the symmetric group on
$\{1,\dots,N\}$.
Fix a group $G$ and a number $d$. For $(g_1,\dots,g_d)\in G^d$ and $x\in G$, define
...
16
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1answer
752 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 ...
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4answers
899 views
Is there an infinite group with exactly two conjugacy classes?
Is there an infinite group with exactly two conjugacy classes?
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3answers
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Characters of p-groups
Berkovich mentioned the following result of Mann in his book on p-groups:
The number of nonlinear irreducible characters of given degree in a p-group is divided by p-1.
Do you know any reference for ...
5
votes
5answers
754 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 ...
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0answers
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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 ...
