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...

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...

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

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

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...

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

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...

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...

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

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...

unique finite group G with the property that for C any nontrivial conjugacy class, every element of G is equal to xy for some x, y in C. Janko found...

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...

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...

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...

certain representations of the Weyl group W associated to unipotent conjugacy classes of a semisimple algebraic group G. There is another parameter involved...

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

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...

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

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

(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...

^{-1}\gamma \delta y)} where γ {\displaystyle \gamma } is an element of the conjugacy class o {\displaystyle o} , and Γ γ {\displaystyle \Gamma _{\gamma }} is...

five conjugacy classes have representatives e, (12)(34), (12), (123), (1234) and, of these, the Möbius configuration corresponds to the conjugacy class e...

reflection is a translation by a reflected translation vector Thus the conjugacy class within the Euclidean group E(n) of a translation is the set of all...