Browsing by Author "Agigor-Mike, Precious Ugonwanyi"

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    Some deductions from the factorization of finite simple groups
    (Federal University of Technology, Owerri, 2017-07) Agigor-Mike, Precious Ugonwanyi
    This 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 ( ) ( ) ( ) * +