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...

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...

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

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...

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...

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...

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

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

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...

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...

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...

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...

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...

G {\displaystyle G} is a symmetric group and the monodromy classes are the conjugacy class of transpositions). Let G {\displaystyle G} be a finite group...

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...

distinguish three kinds of permutations of the three blocks, the conjugacy classes of the group: no change (), a group element of order 1 interchanging...

faithful linear representations of M11 over any field. There are 5 conjugacy classes of maximal subgroups of M11 as follows: M10, order 720, one-point...

PGL(3,4) both sets of subgroups form single conjugacy classes, but in M21 both sets split into 3 conjugacy classes. The subgroups respectively have orbits...

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

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

classification of the 2-dimensional space groups: For each geometric class, the possible arithmetic classes are None: no reflection lines Along: reflection lines along...

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...

double cover of the subgroup M22. Magliveras (1971) found the 12 conjugacy classes of maximal subgroups of HS as follows: Traces of matrices in a standard...

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

{\displaystyle p} -block B {\displaystyle B} is canonically associated a conjugacy class of p {\displaystyle p} -subgroups, called the defect groups of B {\displaystyle...

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

f(u)*f(v)=f(u*v).} The image under an automorphism of a conjugacy class is always a conjugacy class (the same or another). The composition of two automorphisms...