Self-normalizing Sylow subgroups |
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| Authors: | Robert M Guralnick Gunter Malle Gabriel Navarro |
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| Institution: | Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113 ; FB Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str.~40, D--34132 Kassel, Germany ; Departament d'Algebra, Facultat de Matemátiques, Universitat de València, 46100 Burjassot, València, ~Spain |
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| Abstract: | Using the classification of finite simple groups we prove the following statement: Let  be a prime,  a group of automorphisms of  -power order of a finite group  , and  a  -invariant Sylow  -subgroup of  . If  is trivial, then  is solvable. An equivalent formulation is that if  has a self-normalizing Sylow  -subgroup with  a prime, then  is solvable. We also investigate the possibilities when  . |
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