equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under b = g a g − 1 {\displaystyle...

In abstract algebra, a conjugacy class sum, or simply class sum, is a function defined for each conjugacy class of a finite group G as the sum of the elements...

radians. Vertices in the same polyhedron are in the same conjugacy class. Since the conjugacy class equation for A5 is 1 + 12 + 12 + 15 + 20 = 60, we obtain...

a group is said to have the infinite conjugacy class property, or to be an ICC group, if the conjugacy class of every group element but the identity...

an even polygon there are two sets of axes, each corresponding to a conjugacy class: those that pass through two vertices and those that pass through two...

a map of arrows. By definition, an element is central whenever its conjugacy class contains only the element itself; i.e. Cl(g) = {g}. The center is the...

representation on the respective conjugacy class of G. The columns are labelled by (representatives of) the conjugacy classes of G. It is customary to label...

two conjugacy classes for each trace (clockwise and counterclockwise rotations), for absolute value of the trace equal to 2 there are three conjugacy classes...

parity-sensitive conjugacy classes, whose elements always differ when conjugated with any even element versus any odd element. Commutator Conjugacy class Coset Optimal...

this way), so the conjugacy class of g in the Galois group is canonically associated to p. This is called the Frobenius conjugacy class of p and any element...

constitutes an embedding into Dickson's group G2(4). There is only one conjugacy class of J2 in G2(4). Every subgroup J2 contained in G2(4) extends to a subgroup...

direction form a conjugacy class; the translation group is the union of those for all distances. In 1D, all reflections are in the same class. In 2D, rotations...

its Frobenius element, which is a representative of a well-defined conjugacy class in the Galois group Gal(K/Q). Then the theorem says that the asymptotic...

finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups...

conjugacy classes of group elements. The entries consist of characters, the traces of the matrices representing group elements of the column's class in...

order is cyclic. Any element of conjugacy class 3A56 generates Sylow 3-subgroup. Any element from the conjugacy classes 7A24, 7B24 generates the Sylow...

subgroups. class function A class function on a group G is a function that it is constant on the conjugacy classes of G. class number The class number of...

It follows that each conjugacy class in G × H is simply the Cartesian product of a conjugacy class in G and a conjugacy class in H. Along the same lines...

triple cover which is the centralizer of an element of order 3 in M (in conjugacy class "3A") Fi23 is a subgroup of Fi24′ Fi22 has a double cover which is...

group. The 120 symmetries fall into 10 conjugacy classes. Each line in the following table represents one class of conjugate (i.e., geometrically equivalent)...

of deck transformations and H1, H2 are subgroups of G meeting each conjugacy class of G in the same number of elements, then the manifolds H1 \ M and...

center of NG can be described in terms of those elements of G whose conjugacy class is finite. In particular, if the identity element of G is the only...

H representing stable conjugacy classes, such that the stable conjugacy class of G is the transfer of the stable conjugacy class of H, κ is a character...

the number of conjugacy classes of G . {\displaystyle G.} However, because a compact group has in general infinitely many conjugacy classes, this does not...

the Frobenius is wF. The GF conjugacy classes of F-stable maximal tori of G can be identified with the F-conjugacy classes of W, where we say w∈W is F-conjugate...

conjugation: Inner automorphism, a type of conjugation homomorphism Conjugacy class in group theory, related to matrix similarity in linear algebra Conjugation...

representation theory of groups, a class function is a function on a group G that is constant on the conjugacy classes of G. In other words, it is invariant...

to conjugacy classes in 2.B (an order 2 extension of the baby monster group), and the nodes of E ~ 6 {\displaystyle {\tilde {E}}_{6}} to conjugacy classes...

If g in G is not in the center its conjugacy class is exactly g and εg. Thus there are 2N − 1 + 1 conjugacy classes for N odd and 2N − 1 + 2 for N even...

must send each conjugacy class (characterized by the cyclic structure that its elements share) to a (possibly different) conjugacy class. Second, show...