6533b831fe1ef96bd1299148
RESEARCH PRODUCT
Self-normalizing Sylow subgroups
Gabriel NavarroGunter MalleRobert M. Guralnicksubject
CombinatoricsNormal p-complementFinite groupLocally finite groupApplied MathematicsGeneral MathematicsSylow theoremsClassification of finite simple groupsAutomorphismMathematicsdescription
Using the classification of finite simple groups we prove the following statement: Let p > 3 p>3 be a prime, Q Q a group of automorphisms of p p -power order of a finite group G G , and P P a Q Q -invariant Sylow p p -subgroup of G G . If C N G ( P ) / P ( Q ) \mathbf {C}_{\mathbf {N}_G(P)/P}(Q) is trivial, then G G is solvable. An equivalent formulation is that if G G has a self-normalizing Sylow p p -subgroup with p > 3 p >3 a prime, then G G is solvable. We also investigate the possibilities when p = 3 p=3 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-08-07 |