Every p-subgroup is conjugate to a p-subgroup whose normalizer in the Sylow is Sylow in its normalizer

From Groupprops
Revision as of 15:59, 24 March 2008 by Vipul (talk | contribs) (New page: ==Statement== Suppose <math>G</math> is a finite group and <math>S</math> is a <math>p</math>-Sylow subgroup of <math>G</math>. Suppose <math>T</math> is a subgroup contained insi...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Statement

Suppose G is a finite group and S is a p-Sylow subgroup of G. Suppose T is a subgroup contained inside S. Then, there exists a subgroup U of S, such that T and U are conjugate subgroups inside G, and such that N_S(U) is a Sylow subgroup of N_G(U).