dc.contributor.advisor Moori, J. dc.contributor.author Perumal, P. dc.date.accessioned 2021-02-23T11:37:18Z dc.date.available 2021-02-23T11:37:18Z dc.date.issued 2018 dc.identifier.uri http://hdl.handle.net/10394/36760 dc.identifier.uri https://orcid.org/0000-0003-1497-8192 dc.description PhD (Mathematics), North-West University, Mafikeng Campus, 2018 en_US dc.description.abstract The Double Frobenius group is the result of the action of a Frobenius group H = NH, with en_US kernel N and complement H, on a finite group G. If the action of H on G is such that, N acts fixed point free on G and GN is also a Frobenius group with kernel G and complement N, then G = GNH = G: (N:H) = (G:N ):H is a double Frobenius group. In this study we briefly describe the structure of the double Frobenius group and then construct in general two double Frobenius groups which have the form 2n:(Z2n-1:Zn), where n is a prime such that 2n - 1 is a Mersenne prime and 22r:(Z2r_1:Z2), where 2 :S r EN respectively. We then proceed to analyse the two double Frobenius groups mentioned above, calculating the conjugacy classes, Fischer matrices and character table of the groups. The study is concluded by demonstrating these calculations of the conjugacy classes, Fischer matrices and character tables of two examples of each type of double Frobenius group, namely, 23:(Z7:Z3) and 25 :(Z31 :Zs) for the type 2n:(Z2n_ 1 :Zn) with n = 3 and n = 5 respectively, and 24:(Z3:Z2) and 26:(Z7:Z2) for the type 22r:(Z2r-1 :Z2) with r = 2 and r = 3 respectively dc.language.iso en en_US dc.publisher North-West University (South Africa) en_US dc.title On the double frobenius groups and their characters en_US dc.type Thesis en_US dc.description.thesistype Doctoral en_US dc.contributor.researchID 16434188 - Moori, Jamshid (Supervisor)
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