Agigor-Mike, Precious Ugonwanyi2026-03-252026-03-252017-07Agigor-Mike, P. U. (2017). Some deductions from the factorization of finite simple group [Unpublished Master's Thesis]. Federal University of Technology, Owerri, Nigeriahttps://repository.futo.edu.ng/handle/20.500.14562/2483This thesis is for the award of Master of Science (M.Sc.) in Pure MathematicsThis work looked into the factorization of minimal normal subgroups of innately transitive groups. It was shown that if , is a finite set of primes and if M is a non-abelian characteristically simple group with simple normal subgroups and ( * +) is a full factorization of M then (i) the pair ( * ( ) ( )+) forms -groups (ii) the subgroups ( ) and ( ) cannot have normal -complements in and that ( ) and ( ) are not - complements of each other. Again from the results of Baddeley and Praeger it showed that and are full diagonal subgroups of M. If and are self normalizing subgroups in M and not isomorphic to ( ) , ( ) , ( ), then and are maximal nilpotent subgroups of M. Further, and are conjugates and therefore solvable groups. It further showed that if G is a finite simple group with a transitive minimal normal subgroup M where M is characteristically simple and can be expressed as and if and are proper subgroups of M, then ( * +) is a full factorization such that for all , the pair ( * ( ) ( )+) is a full factorization and ( ) and ( ) are conjugates * +, ( ) * + and ( ) ( ) ( ) * +enAttribution-NonCommercial-ShareAlike 4.0 InternationalMinimal normal subgroupsfinite simple groupscentralizersnormalizersDepartment of MathematicsMaster’s Thesis