caa a22 4500 475807561 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1008319107762 doi (NATIONALLICENCE)springer-10.1023/A:1008319107762 Perfect Baer Subplane Partitions and Three-Dimensional Flag-Transitive Planes [Elektronische Daten] [R. Baker, J. Dover, G. Ebert, K. Wantz] The classification of perfectBaer subplane partitions of PG(2, q2) is equivalentto the classification of 3-dimensional flag-transitive planeswhose translation complements contain a linear cyclic group actingregularly on the line at infinity. Since all known flag-transitiveplanes admit a translation complement containing a linear cyclicsubgroup which either acts regularly on the points of the lineat infinity or has two orbits of equal size on these points,such a classification would be a significant step towards theclassification of all 3-dimensional flag-transitive planes. Usinglinearized polynomials, a parametric enumeration of all perfectBaer subplane partitions for odd q is described.Moreover, a cyclotomic conjecture is given, verified by computerfor odd prime powers q < 200, whose truth would implythat all perfect Baer subplane partitions arise from a constructionof Kantor and hence the corresponding flag-transitive planesare all known. Kluwer Academic Publishers, 2000 Baer subplane nationallicence flag-transitive affine plane nationallicence linearized polynomials nationallicence Baker R. Department of Mathematics, West Virginia State College Institute, 25112-1000, WV aut Dover J. Department of Mathematics, North Dakota State University, 58105-5075, Fargo, ND aut Ebert G. Department of Math Sciences, University of Delaware, 19716, Newark, DE aut Wantz K. Department of Mathematics, Southern Nazarene University, 73008, Bethany, OK aut Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 19-39 0925-1022 21:1-3<19 2000 21 10623 https://doi.org/10.1023/A:1008319107762 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008319107762 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baker R. Department of Mathematics, West Virginia State College Institute, 25112-1000, WV aut NATIONALLICENCE 700 1- Dover J. Department of Mathematics, North Dakota State University, 58105-5075, Fargo, ND aut NATIONALLICENCE 700 1- Ebert G. Department of Math Sciences, University of Delaware, 19716, Newark, DE aut NATIONALLICENCE 700 1- Wantz K. Department of Mathematics, Southern Nazarene University, 73008, Bethany, OK aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 19-39 0925-1022 21:1-3<19 2000 21 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer