Classical involution theorem
Encyclopedia
In mathematical finite group theory, the classical involution theorem of classifies simple group
s with a classical involution
and satisfying some other conditions, showing that they are mostly groups of Lie type
over a field
of odd characteristic. extended the classical involution theorem to groups of finite Morley rank.
A classical involution t of a finite group G is an involution whose centralizer has a subnormal subgroup containing t with quaternion Sylow 2-subgroups.
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...
s with a classical involution
Involution
In mathematics, an involution, or an involutary function, is a function f that is its own inverse:-General properties:Any involution is a bijection.The identity map is a trivial example of an involution...
and satisfying some other conditions, showing that they are mostly groups of Lie type
Group of Lie type
In mathematics, a group of Lie type G is a group of rational points of a reductive linear algebraic group G with values in the field k. Finite groups of Lie type form the bulk of nonabelian finite simple groups...
over a field
Field (mathematics)
In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
of odd characteristic. extended the classical involution theorem to groups of finite Morley rank.
A classical involution t of a finite group G is an involution whose centralizer has a subnormal subgroup containing t with quaternion Sylow 2-subgroups.