In mathematical

finite Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

, the classical involution theorem of classifies

simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The d ...

s with a classical

involution Involution may refer to: * Involute, a construction in the differential geometry of curves * '' Agricultural Involution: The Processes of Ecological Change in Indonesia'', a 1963 study of intensification of production through increased labour inpu ...

and satisfying some other conditions, showing that they are mostly

groups of Lie type In mathematics, specifically in group theory, the phrase ''group of Lie type'' usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phras ...

over a

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

of odd characteristic. extended the classical involution theorem to

groups of finite Morley rank In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley rank (see below). Examples *A group of finite Morley rank is an abstract group '' ...

. A classical involution ''t'' of a finite group ''G'' is an involution whose centralizer has a

subnormal subgroup In mathematics, in the field of group theory, a subgroup ''H'' of a given group ''G'' is a subnormal subgroup of ''G'' if there is a finite chain of subgroups of the group, each one normal in the next, beginning at ''H'' and ending at ''G''. In not ...

containing ''t'' with quaternion Sylow 2-subgroups.

References

* * * * Theorems about finite groups {{group-theory-stub