## Lectures on Subgroups of Sylow Type in Finite Soluble GroupsDepartment of Pure Mathematics, School of General Studies and Department of Mathematics, Institute of Advanced Studies, A.N.U., 1979 - Finite groups - 100 pages |

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abelian assumed automorphisms avoided belongs called cap subgroup Carter centralized chief factor class of groups clearly conjugate under H construction contains contradiction Corollary covered Definition Let equivalent example exists factor of G finite follows follows immediately Frattini argument Furthermore given group G Hall hence holds hypothesis implies induction injectors isomorphic known Let G Let X Li+1 maximal minimal normal subgroup NG(S nilpotent normal Fitting class normal subgroup obviously otherwise p-chief p-group p-subgroup particular permutation precisely primitive class primitive factor groups primitive groups projectors Proof proved Q-perfect Remarks respectively saturated formation Schunck class Si+1 soluble groups subgroup of G subnormal monomorphisms Sylow N-subgroup Theorem Let theory treated X-injector X-maximal in G X-projector of G yields