## P-Normally Embedded Subgroups of Finite Soluble Groups |

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### Contents

Preliminaries and known results concerning formations | 2 |

Preliminaries concerning Fitting classes | 12 |

pnormally embedded subgroups | 15 |

3 other sections not shown

### Common terms and phrases

abelian Sylow p-subgroup avoids each chief Carter and Hawkes Carter subgroups chief series complements conjugacy class conjugate Corollary cover-avoidance property covers and avoids covers or avoids embedded in G factors of G finite soluble group Fischer class Fitting classes Frattini subgroup G and avoids G are p-normally G has p-length Hall subgroups induction on g injector of G integrated local definition ir-group Let G locally defined main theorems maximal in G maximal subgroup minimal normal subgroup nilpotent groups nonempty normal in G normalizers of A-groups p-chief p-group p-normally embedded subgroups p-power index pne-G proceed by induction projector of G pronormal in G pronormal subgroups Proof of Theorem prove Theorem quaternion group result Rose 24 saturated formation Schur-Zassenhaus Theorem subgroup of G Suppose G Sylow systems system normalizers Theorem 5.2 thesis unique minimal normal V-pne-G VN/N Vp be Sylow x e G