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Conjugacy classes may be referred to by describing them, or more briefly by abbreviations such as "6A", meaning "a certain conjugacy class with elements of order 6", and "6B" would be a different conjugacy class with elements of order 6; the conjugacy class 1A is the conjugacy class of the identity which has order 1.
All the reflections are conjugate to each other whenever n is odd, but they fall into two conjugacy classes if n is even. If we think of the isometries of a regular n-gon: for odd n there are rotations in the group between every pair of mirrors, while for even n only half of the mirrors can be reached from one by these rotations. Geometrically ...
If a finite group G has exactly two conjugacy classes of involutions with representatives t and z, then the Thompson order formula (Aschbacher 2000, 45.6) (Suzuki 1986, 5.1.7) states
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The symmetric group S4, consisting of all 24 permutations of four elements, has five conjugacy classes. And you can compute that there are five conjugacy classes by taking the integer partition of 4. But how can you compute how many elements each conjugacy class has? PJ Geest 14:56, 1 June 2009 (UTC)
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 in that conjugacy class. The class sums of a group form a basis for the center of the associated group algebra .
CC Sabathia, who pitched the last 11 seasons of his 19-year Major League career in New York, will be wearing a Yankees cap in his Hall of Fame plaque. The National Baseball Hall of Fame and Museum ...
Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to communicate information about many musical elements, including pitch, duration, dynamics, or articulation of musical notes; tempo, metre, form (e.g., whether sections are repeated), and details about specific playing techniques (e.g., which ...