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 O"p"′("G"), then it is defined to be "p"-constrained if the "p"-core O"p"("G") contains its centralizer, or in other words if its generalized Fitting subgroup is a "p"-group. More generally, if O"p"′("G") is non-trivial, then "G" is called "p"-constrained if "G"/ O"p"′("G") is "p"-constrained.
All "p"-solvable groups are "p"-constrained.