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)
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