OSU Navigation Bar

The Ohio State University University Libraries Knowledge Bank

The Knowledge Bank is scheduled for regular maintenance on Sunday, April 20th, 8:00 am to 12:00 pm EDT. During this time users will not be able to register, login, or submit content.

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

Show simple item record

Files Size Format View
V71N03_170.pdf 379.0Kb PDF View/Open

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