# conjugate elements

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## conjugate elements

[′kän·jə·gət ′el·ə·mənts]
(mathematics)
Two elements a and b in a group G for which there is an element x in G such that ax = xb.
Two elements of a determinant that are interchanged if the rows and columns of the determinant are interchanged.
References in periodicals archive ?
This implies that the complex conjugation lies in the conjugacy class of [tau].
If H [member of] O (X), then (H) stands for its conjugacy class, referred to as an orbit type.
is thus an element of the conjugacy class of rotations by the angle [alpha], which fully characterizes the motion of a defect described at rest by metric (1).
The conjugacy class of [gamma] [member of] [S.sub.n] contains all the elements of [S.sub.n] with the same cycle type, and the cycle types are in one-to-one correspondence with partitions of n.
The simplest way to look at conjugation with the Group Calculator is to select a group and an element of that group, and then click on Close Under Conj.; the conjugacy class of the element will be highlighted.
For n even there are n+6/2 conjugacy classes organized in five families Conjugacy class Representative Centralizer subgroup {e} e [D.sub.n] {[[rho].sup.n/2]} [[rho].sup.n/2] [D.sub.n] {[[rho].sup.i], [[rho].sup.i] {[[rho].sup.i] | 0 [[rho].sup.-i]}, [less than or equal to] 1 [less than or i < n} equal to] i < n/2 {[[rho].sup.2i] [tau] {e, [tau], [tau]| 0 [[rho].sup.n/2], [less than or [[rho].sup.n/2][tau]} equal to] i < n/2} {[[rho].sup.2i+1] [rho][tau] {e, [rho][tau], [tau]| 0 [[rho].sup.n/2], [less than or [[rho].sup.n/2+1][tau]} equal to] i < n/2}
[[[alpha].sup.S8]], then, is the set of all conjugates of [alpha], or the conjugacy class of [alpha].
lambda], then the conjugacy class C([gamma]) of [gamma] is not contained in the coset [gamma][Kappa][lambda], and so f cannot be supported on C([gamma]).
A fixed point of f is a conjugacy class [q] of configurations such that f([q]) = [q], i.e.
Recall also that the [S.sub.n] conjugacy class of cycle type [zeta], when [zeta] is a partition into distinct odd parts, splits into two conjugacy classes in the alternating group [A.sub.n], which we denote by [[zeta].sup.1] and [[zeta].sup.2].
is a conjugacy invariant, equal to the coefficient, by which the conjugacy class of [theta] enters in the Plancherel formula for [pi].
All c-traces of fixed length and fixed positive excess define a unique conjugacy class.
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