P-constrained group
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.
Definition
If a group has trivial p core Op, then it is defined to be p-constrained if the p-core Op contains its centralizer, or in other words if its generalized [Fitting subgroup] is a p-group. More generally, if Op is non-trivial, then G is called p-constrained if G/Op is.All p-solvable groups are p-constrained.