G2 (mathematics) - Finite Groups

Finite Groups

The group G2(q) is the points of the algebraic group G2 over the finite field Fq. These finite groups were first introduced by Leonard Eugene Dickson in Dickson (1901) for odd q and Dickson (1905) for even q. The order of G2(q) is q6(q6−1)(q2−1). When q≠2, the group is simple, and when q = 2, it has a simple subgroup of index 2 isomorphic to 2A2(32). The J1 was first constructed as a subgroup of G2(11). Ree (1960) introduced twisted Ree groups 2G2(q) of order q3(q3+1)(q−1) for q=32n+1 an odd power of 3.

Read more about this topic:  G2 (mathematics)

Famous quotes containing the words finite and/or groups:

    We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.
    Blaise Pascal (1623–1662)

    Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.
    Zick Rubin (20th century)