In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
Functions that are constant for members of the same conjugacy class are called class functions.
The orbits of this action are the conjugacy classes, and the stabilizer of a given element is the element's centralizer.
en.wikipedia.org /wiki/Conjugacy (896 words)
Conjugacy(Site not responding. Last check: 2007-10-22)
Conjugacy(Site not responding. Last check: 2007-10-22)
Although the conjugacy classes of an abeliangroup are trivial, the standard class functions are provided for completeness.
Construct a set of representatives for the conjugacy classes of G. The classes are returned as a sequence of tuples containing the class length, the order of the elements in the class and a representative element for the class.
The power map M associated with the conjugacy classes of G. Let x be a representative of class number c in G and let n be any integer.
Construct a set of representatives for the conjugacy classes of G. The classes are returned as a sequence of triples containing the element order, the class length and a representative element for the class.
Al := "Random": Construct the conjugacy classes of elements for a permutation group G using an algorithm that searches for representatives of all conjugacy classes of G by examining a random selection of group elements and their powers.
Given a group G for which the conjugacy classes are known and an element x of G, return the designated representative for the conjugacy class of G containing x.
Representatives for the conjugacy classes of elementary abeliansubgroups for the group G. The subgroups are returned as a sequence of records having the same format as
The elements of the poset correspond to the conjugacy classes of subgroups.
The number of elements of the conjugacy class of subgroups e that lie in a fixed representative of the conjugacy class of subgroups f.
The designated representative for the conjugacy class of G containing the element x (relative to existing conjugacy classes).
Given a group G and elements g and h belonging to G, return the value true if g and h are conjugate in G. The function also returns a second value in the event that the elements are conjugate: an element z which conjugates g into h.
The power map M associated with the conjugacy classes of G. M describes where the elements of the conjugacy classes of G move under powers.
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Subject: Direct correspondence between irreps and conjugacy classes in finite Date: Tue, 19 Oct 1999 09:17:39 +0200 Newsgroups: sci.math.research Let G be a finite group.
It is then a fundamental well-known result that the set of irreducible complex representations of G and the set of conjugacy classes of G have the same cardinality.
The conjugacy classes also form and E_8 graph if you resolve the singularity of the algebraic surface C^2/Gamma.
, testing conjugacy is performed by transforming each element into a standard representative of its conjugacy class by an orbit-stabilizer process that works down a sequence of increasing quotients of G. Conjugacy testing for a group G in category
Given a group G, construct the conjugacy classes and the class map f for G. For any element x of G, f(x) will be the index of the conjugacy class of x in the sequence returned by the
: Construct the conjugacy classes of elements for a permutation or matrix group G using an algorithm that searches for representatives of all conjugacy classes of G by examining a random selection of group elements and their powers.
In nonlinear dynamics, it is often advantageous to establish a conjugacy or a semiconjugacy between the dynamical system in question and the dynamics on some symbol space.
The properties of the dynamical system are usually easy to see in the symbol space and, by the conjugacy or semiconjugacy, these properties must also exist in the original dynamical system.
Our notions of topological conjugacy and symbolic dynamics give us a promising way to analyze chaotic behavior in a specific dynamical system.
The elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes reveals many important features of a group's structure.
Two elements a and b of G are called conjugate iff there exists an element g in G with g
Every element of the group belongs to precisely one conjugacy class.
Conjugacy(Site not responding. Last check: 2007-10-22)
Given a group G, construct the conjugacy classes and the class map f for G. For any element x of G, f(x) will be the conjugacy class representative chosen by the
: Construct the conjugacy classes of elements for a matrix group G using an algorithm that searches for representatives of all conjugacy of G by examining a random selection of group elements and their powers.
The number of conjugacy classes of elements for the group G. PowerMap(G) : GrpMat -> Map
