equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under b = g a g − 1 {\displaystyle...
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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...
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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...
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Alternating group (section Conjugacy classes)
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...
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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...
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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...
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SL2(R) (section Conjugacy classes)
two conjugacy classes for each trace (clockwise and counterclockwise rotations), for absolute value of the trace equal to 2 there are three conjugacy classes...
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Rubik's Cube group (section 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...
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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...
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Symmetric group (section Conjugacy classes)
finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups...
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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...
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Janko group J2 (section Conjugacy classes)
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...
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Euclidean group (section Conjugacy classes)
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...
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conjugacy classes of group elements. The entries consist of characters, the traces of the matrices representing group elements of the column's class in...
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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...
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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...
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Dihedral group of order 6 (section Conjugacy classes)
distinguish three kinds of permutations of the three blocks, the conjugacy classes of the group: no change (), a group element of order 1 interchanging...
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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...
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Deligne–Lusztig theory (section Geometric conjugacy)
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...
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Mathieu group M11 (section Conjugacy classes)
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...
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McLaughlin sporadic group (section Conjugacy classes)
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...
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Icosahedral symmetry (section Conjugacy classes)
group. The 120 symmetries fall into 10 conjugacy classes. Each line in the following table represents one class of conjugate (i.e., geometrically equivalent)...
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Higman–Sims group (section 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...
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Mathieu group M24 (section Conjugacy classes)
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...
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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...
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Mathieu group M22 (section Conjugacy classes)
stabilizer of M11 (point in orbit of 12) There are 12 conjugacy classes, though the two classes of elements of order 11 are fused under an outer automorphism...
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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...
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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...
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must send each conjugacy class (characterized by the cyclic structure that its elements share) to a (possibly different) conjugacy class. Second, show...
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the number of conjugacy classes of G . {\displaystyle G.} However, because a compact group has in general infinitely many conjugacy classes, this does not...
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