ZJ theorem

In mathematics, George Glauberman's ZJ theorem states that if a finite group G is p-constrained and p-stable and has a normal p-subgroup for some odd prime p, then Op(G)Z(J(S)) is a normal subgroup of G, for any Sylow p-subgroup S.

Notation and definitions

References

  • Glauberman, George (1968), "A characteristic subgroup of a p-stable group", Canadian Journal of Mathematics, 20: 1101–1135, doi:10.4153/cjm-1968-107-2, ISSN 0008-414X, MR 0230807
  • Gorenstein, D. (1980), Finite Groups, New York: Chelsea, ISBN 978-0-8284-0301-6, MR 0569209
  • Thompson, John G. (1969), "A replacement theorem for p-groups and a conjecture", Journal of Algebra, 13: 149–151, doi:10.1016/0021-8693(69)90068-4, ISSN 0021-8693, MR 0245683


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