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.
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- Chermak, Andrew (2004), "Quadratic pairs", Journal of Algebra, 277 (1): 36–72, doi:10.1016/S0021-8693(03)00334-X, ISSN 0021-8693, MR 2059620
- Thompson, John G. (1971), "Quadratic pairs", Actes du Congrès International des Mathématiciens (Nice, 1970), vol. 1, Gauthier-Villars, pp. 375–376, MR 0430043