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...

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 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...

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

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...

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...

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

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...

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...

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...

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...

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

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...

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

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

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

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...

specifies the irreducible character, while the partition ρ specifies the conjugacy class on whose group elements the character is evaluated to produce the character...

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...

group 3.McL:2 is a maximal subgroup of the Lyons group. McL has one conjugacy class of involution (element of order 2), whose centralizer is a maximal...

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...

(here χ1 denotes the trivial character). Because g is not in the same conjugacy class as 1, the orthogonality relation for the columns of the group's character...

same conjugacy class of π1(R) can be deformed continuously to each other, and hence, distinct defects correspond to distinct conjugacy classes. Poénaru...

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...

the class equation; it relates the order of a finite group G to the order of its center Z(G) and the sizes of its non-trivial conjugacy classes: | G...

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...

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