The order of group is 168 = 3 * 7 * 8, this implies existence of centralizer of any element from the conjugacy class 2 " A " 21.
32.
For example, in the general linear group, the centralizer of any subset is Zariski connected, so the L-packets for the general linear group all have 1 element.
33.
An image of a dodecad has a centralizer of type 2 11 : M 12 : 2, which is contained in a maximal subgroup of type 2 11 : M 24.
34.
It is named after the Swiss mathematicians Armand Borel and Jean de Siebenthal who developed the theory in 1949 . Each such subgroup is the identity component of the centralizer of its center.
35.
To motivate it, consider the problem of trying to find a normal subgroup " H " of " G " that contains its own centralizer and the Fitting group.
36.
For "'connected algebraic groups "'over an algebraically closed field a "'Cartan subgroup "'is usually defined as the centralizer of a maximal torus.
37.
Thus the number of elements in the conjugacy class of is the index of the centralizer in & # 8239;; hence the size of each conjugacy class divides the order of the group.
38.
Where the sum is over all of the irreducible characters of and the symbol " C G " ( " g " ) } } denotes the order of the centralizer of.
39.
They have involution centralizers of the form, and by investigating groups with an involution centralizer of the similar form Janko found the sporadic group " J " 1 . determined their maximal subgroups.
40.
The obvious choice for such a subring is the centralizer " Z " of, the subring of all matrices that commute with; by definition is in the center of " Z ".
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