Quadratic pair

Short description: Mathematical Quadratic formula

In mathematical finite group theory, a quadratic pair for the odd prime p, introduced by (Thompson 1971), is a finite group G together with a quadratic module, a faithful representation M on a vector space over the finite field with p elements such that G is generated by elements with minimal polynomial (x − 1)². Thompson classified the quadratic pairs for p ≥ 5. (Chermak 2004) classified the quadratic pairs for p = 3. With a few exceptions, especially for p = 3, groups with a quadratic pair for the prime p tend to be more or less groups of Lie type in characteristic p.

See also

• p-stable group

References

• Chermak, Andrew (2004), "Quadratic pairs", Journal of Algebra 277 (1): 36–72, doi:10.1016/S0021-8693(03)00334-X, ISSN 0021-8693 
• Thompson, John G. (1971), "Quadratic pairs", Actes du Congrès International des Mathématiciens (Nice, 1970), 1, Gauthier-Villars, pp. 375–376