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...

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...

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...

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...

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

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...

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

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...

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...

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...

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...

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...

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...

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...

mathematics, class number may refer to Class number (group theory), in group theory, is the number of conjugacy classes of a group Class number (number...

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

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...

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...

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

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...

(q–2)/2 conjugacy classes of non-trivial elements. Cyclic subgroups of order q+2r+1, of index 4 in their normalizers. These account for (q+2r)/4 conjugacy classes...

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...

3) is isomorphic to the Möbius group PSL(2, C), its conjugacy classes also fall into five classes: Elliptic transformations Hyperbolic transformations...

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

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