Component theorem
Encyclopedia
In the mathematical
classification
of finite simple groups, the component theorem of shows that if G is a simple group
of odd type, and various other assumptions are satisfied, then G has a centralizer of an involution with a "standard component" with small centralizer.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
classification
Classification theorem
In mathematics, a classification theorem answers the classification problem "What are the objects of a given type, up to some equivalence?". It gives a non-redundant enumeration: each object is equivalent to exactly one class....
of finite simple groups, the component theorem of shows that if G is a simple group
Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, a normal subgroup and the quotient group, and the process can be repeated...
of odd type, and various other assumptions are satisfied, then G has a centralizer of an involution with a "standard component" with small centralizer.