Finite Conjugacy

Views Updated: Dec 15, 2025

Abbreviation

Pronunciation

/ˈfaɪnaɪt ˈkɒndʒʊɡəsi/

Using the theory of elementary group and character, we get a result to characterize the structure of finite groups when the average length of conjugacy classes of the finite groups is given. This is significant for studying the quantitative property of finite groups.
The second part : We study the connection between a non-abelian finite p-group G and the number of conjugacy class of it. We also find some more concise relationships between the minor order of a non-abelian finite p-group G and the number of conjugacy class of it.
Finite Groups Whose Monolithic Characters Vanish on at Most Two Conjugacy Classes
Let G be a finite group, | x | be the length of conjugacy clas containing x.
In particular, for a finite group G, every simple module of G is appeared in the conjugacy representation of G if and only if the sum of every row in the character table of G is not zero.

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