Another less common notation for the centralizer is Z ( " a " ), which parallels the notation for the center of a group.
22.
The C-groups include as special cases the CIT-groups, that are groups in which the centralizer of any involution is a 2-group.
23.
Characterized the Rudvalis group by the centralizer of a central involution . gave another characterization as part of their identification of the Rudvalis group as one of the quasithin groups.
24.
Since the Fitting subgroup of a finite solvable group contains its own centralizer, this gives a method of understanding finite solvable groups as faithful automorphism groups of nilpotent groups.
25.
The so-called " rigidity " states that the identity component of the centralizer of a diagonalizable group coincides with the identity component of the normalizer of the group.
26.
From the theorem of Borel and de Siebenthal, the involution ? is inner and " K " is the centralizer of a torus " S ".
27.
The idea is that these groups have a centralizer of an involution with a component that is a smaller quasisimple group, which can be assumed to be already known by induction.
28.
So to classify these groups one takes every central extension of every known finite simple group, and finds all simple groups with a centralizer of involution with this as a component.
29.
If is a finite group, then for any group element, the elements in the conjugacy class of are in one-to-one correspondence with cosets of the centralizer.
30.
In ring theory, the "'centralizer of a subset of a ring "'is defined with respect to the semigroup ( multiplication ) operation of the ring.
