A non-simplicity criterion of finite groups

dc.contributor.authorKambira, Fredie Joshua Jonny
dc.description.abstractCharacterization of groups is normally done in two ways: by considering the structure of the group directly or by looking at the “local” properties of the group. Group theory and character theory are necessary for both methods. This research is a continuation of the characterization problem by looking at a local property of an abstract finite group G. We consider the following problem: Let G be a finite group with H a maximal subgroup satisfying (i) H = XP<t>, where x = R x S, R has odd order, S is a 2-group, P = <x> is cyclic of order 3, And t2 = (xt)2 = 1. (ii) X acts fixed-point-free on S; S # 1. (iii) H is the only maximal subgroup of G containing K = (R x S) P and [W1z(s)]>4. It is established that such a finite group G is non-simple. In one of the recent works, A.A. Liggonah considers a finite group G with a maximal subgroup H satisfying the hypotheses given in [24] and establishes that G is non-simple. In particular, he considers P to be an elementary abelian sylow 3-subgroup of order 9. G. Higman establishes, for G satisfying the same conditions as in [24] but with P being a cyclic sylow 3-subgroup of order 3, that G is non-simple; (refer [16].en_US
dc.identifier.citationKambira, F. J. J. (1982) A non-simplicity criterion of finite groups, Masters dissertation, University of Dar es Salaam. Available at (
dc.publisherUniversity of Dar es Salaamen_US
dc.subjectFinite groupsen_US
dc.subjectDifference equationsen_US
dc.subjectTheory ofen_US
dc.titleA non-simplicity criterion of finite groupsen_US