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admitting groups fixing one Baer subgeometry and acting transitively on the remaining Baer subgeometries. ... When q is even, we show that a Baer subgeometry partition of PG(2, q 2 ) with a group fixing one and transitive on the remaining PG(2, q)'s forces the partition to be classical or q=4 and the partition ... Moreover, we discuss ''transitive'' deficiency one partial Baer subgeometry partitions; deficiency one partial BSG's admitting a group transitive on the subplanes of the partition. ...doi:10.1006/jcta.2001.3232 fatcat:qeviqsx7obfpljyg3637wcug3y
| (1-IA; Iowa City, IA) Transitive deficiency-one Baer subgeometry partitions. (English summary) J. Combin. Theory Ser. A 98 (2002), no. 1, 127-149. ... A Baer subgeometry partition (BSG) of a finite projective space PG(2k,q7) is a partition of its points by Baer subspaces (isomor- phic to PG(2k,q)). The authors refer to a result of N. ...
Korchmáros, Transitive ovoids of the Hermitian surface E. Kuijken, Distance-regular geometries I.N. Landjev, On arcs in projective Hjelmslev planes over finite chain rings D. ... Leemans, RWPRI and (2T ) 1 flag-transitive linear spaces G. Lunardon, Spreads in H(q) and 1-systems of Q(6, q) D. Luyckx, On 1-systems of Q(6, q), q even R. Meshulam, Group algebras and expanders K. ... subgeometries PG(4,q). ...doi:10.1007/s10623-007-9162-6 fatcat:yd5cqfmlrfa7zlzeifhhx7qfg4
Non-normalizing Baer involutions. (English summary) 2003e:51017 — (with Johnson, Norman Lloyd!) Transitive deficiency-one Baer subgeometry partitions. ... (with Pomareda, Rolando) Transitive partial parallelisms of deficiency one. ...
We characterize the Miquelian Laguerre planes as those admitting a group containing a non-trivial elation and acting transitively on flags, with an additional hypothesis-a quasiprimitive action on circles ... This had a profound effect on the study of geometry, eventually elevating symmetry to a central role. ... involution, 28, 98 Baer subgeometry, 97 Baer subplanes, 28 Baer subspaces, 27 base, 47 blank type I, 13 blank type II, 13 block design, 24 block-tactical, 100 Buekenhout-Metz unitals, 29 bundle, 72 bundle ...fatcat:dcihwewq7ncetffyooqv43dohm