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 *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.

See also

p-stable group

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

References

Gorenstein, D.; Walter, John H. (1964), "On the maximal subgroups of finite simple groups", Journal of Algebra, 1: 168–213, doi:10.1016/0021-8693(64)90032-8, ISSN 0021-8693, MR 0172917

Gorenstein, D. (1980), Finite groups (2nd ed.), New York: Chelsea Publishing Co., ISBN 978-0-8284-0301-6, MR 0569209

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