In mathematics, a p-constrained group is a finite group resembling the centralizer of an element of prime order p in a group of Lie type over a finite field of characteristic p. They were introduced by in order to extend some of Thompson's results about odd groups to groups with dihedral Sylow 2-subgroups.
If a group has trivial p core O<sub>p</sub>(G), then it is defined to be p-constrained if the p-core O<sub>p</sub>(G) contains its centralizer, or in other words if its generalized Fitting subgroup is a p-group. More generally, if O<sub>p</sub>(G) is non-trivial, then G is called p-constrained if G/O<sub>p</sub>(G) is .
All p-solvable groups are p-constrained.