Quadratic pair

In mathematical finite group theory, a quadratic pair for the odd prime "p", introduced by , 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 minimum polynomial ("x" − 1)2. Thompson classified the quadratic pairs for "p" ≥ 5. 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