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# Coset Geometries of Some Generalized Semidirect Products of Groups

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/5615

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 dc.creator Payne, Stanley E. en_US dc.date.accessioned 2005-10-01T03:04:42Z dc.date.available 2005-10-01T03:04:42Z dc.date.issued 1971-05 en_US dc.identifier.citation The Ohio Journal of Science. v71 n3 (May, 1971), 170-174 en_US dc.identifier.issn 0030-0950 en_US dc.identifier.uri http://hdl.handle.net/1811/5615 dc.description Author Institution: Department of Mathematics, Miami University, Oxford, Ohio 45056 en_US dc.description.abstract A generalization of the standard semi-direct product of groups is given. The following special case is exploited in the construction of partial 4-gons. Let G be the set of 4-tuples of elements of the finite field F. For all i, j with l < i , j<2, let Ljj and Rij be linear transformations of F over its prime subfield. Then define a product on G as follows: (a1, b1, c1, d1)- (a2, b2, c2, d2) = (ai+a2, b1+b2, L11 R11 L12 R12 L21 R2i L22 R22 a1 b2 +a2 b1 +c1+c2, a1 b2 +a2 b1 +d1+d2). With this product G is a group. Let A and B be the subgroups of G consisting of elements of the form (a, 0, 0, 0), a e F, and (0, b, 0,0), b e F, respectively. Then necessary and sufficient conditions on Lij and Rij are found for the coset geometry ir(G, A, B) to be a partial generalized 4-gon. en_US dc.format.extent 388157 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.rights Reproduction of articles for non-commercial educational or research use granted without request if credit to The Ohio State University and The Ohio Academy of Science is given. en_US dc.title Coset Geometries of Some Generalized Semidirect Products of Groups en_US