P-Normally Embedded Subgroups of Finite Soluble Groups |
Common terms and phrases
abelian Sylow p-subgroup assume assumption avoids H/K Carter and Hawkes Carter subgroups central chief factors coincide complements completes concerning conjugate consequently consider contained cover-avoidance property covers H/K covers or avoids desired eccentric embedded in G example exists extend fact factors of G finite soluble group Fischer class Fitting classes G has p-length Gaschütz Hall subgroup Hall's Hartley hence implies induction on G introduced K-injector of G known locally defined main theorems minimal normal subgroup necessary nonempty normal in G normalizers of A-groups Note p-chief p-group p-normally embedded subgroups p-power index p-soluble preliminary prime proceed by induction projector of G projectors pronormal in G Proof Proposition result saturated formation shown subgroup of G Suppose Suppose G system normalizers Theorem 4.8 thesis true turn unique minimal normal V-pne-G р р