Conjugacy class sum

Let G be a finite group with conjugacy class C. Then the class sum

$\overline{C} = \sum_{c \in C} c$

is an element of the center of the group algebra $Z(\mathbb{C} G)$.

This algebra-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Algebra stubs Group theory Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Strofi USS Frederick Look at other dictionaries: Conjugacy class — In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non abelian groups reveals many important… …   Wikipedia Class function — In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function f on a group G, such that f is constant on the conjugacy classes of G. In other words, f is invariant under the… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia Character theory — This article refers to the use of the term character theory in mathematics. For the media studies definition, see Character theory (Media). In mathematics, more specifically in group theory, the character of a group representation is a function… …   Wikipedia Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… …   Wikipedia Deligne–Lusztig theory — In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ adic cohomology with compact support, introduced by Deligne Lusztig (1976). Lusztig (1984) used these representations to… …   Wikipedia Character table — Main article: Character theory In group theory, a character table is a two dimensional table whose rows correspond to irreducible group representations, and whose columns correspond to classes of group elements. The entries consist of characters …   Wikipedia Automorphisms of the symmetric and alternating groups — In group theory, a branch of mathematics, the automorphisms and outer automorphisms of the symmetric groups and alternating groups are both standard examples of these automorphisms, and objects of study in their own right, particularly the… …   Wikipedia Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia Generalized flag variety — In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”