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 Gorenstein and Walter (1964, p.169) 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 pTemplate:Prime core O_{pTemplate:Prime}(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_{pTemplate:Prime}(G) is non-trivial, then G is called p-constrained if G/O_{pTemplate:Prime}(G) is p-constrained.

All p-solvable groups are p-constrained.

See also

• p-stable group
• The ZJ theorem has p-constraint as one of its conditions.