caa a22 4500 378913786 CHVBK 20180305123548.0 cr unu---uuuuu 161128e20041103xx s 000 0 eng 10.1515/advg.2004.4.4.413 doi (NATIONALLICENCE)gruyter-10.1515/advg.2004.4.4.413 Nuclear fusion in finite semifield planes [Elektronische Daten] [Vikram Jha, Norman L. Johnson] We study the subplanes of finite semifield planes that are coordinatizable by subfields F of some semifield D such that F lies in at least two of the three seminuclear fields N ℓ(D), Nm (D), and Nr (D). Our main results determine completely the combinatorial configurations associated with such subplanes, and enables, for example, a computational method to determine the number of nuclear planes of order q in semifield planes of order qt . The results have a number of applications. Firstly, they imply ‘fusion' theorems. The most basic one is that if two or more seminuclear subfields, of a semifield D coordinatizing a translation plane π, are each isomorphic to GF(q), then π may be recoordinatized by a semifield E such that the indicated seminuclear fields, of order q, coincide. The most important case is nuclear fusion: if all three seminuclei of D are isomorphic to GF(q) then the nucleus N(E) ≅ GF(q). Further applications are concerned with semifield spreads π of order q 2. We classify all such π that admit three homology groups of order q - 1 with dierent axis (the shears axis, the infinite line, and any other component), thus generalizing a theorem of D. E. Knuth, who proved an algebraic version of the result. © de Gruyter Geometry nationallicence Jha Vikram aut Johnson Norman L. aut Advances in Geometry Walter de Gruyter 4/4(2004-11-03), 413-432 1615-715X 4:4<413 2004 4 advg https://doi.org/10.1515/advg.2004.4.4.413 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/advg.2004.4.4.413 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jha Vikram aut NATIONALLICENCE 700 1- Johnson Norman L. aut NATIONALLICENCE 773 0- Advances in Geometry Walter de Gruyter 4/4(2004-11-03), 413-432 1615-715X 4:4<413 2004 4 advg CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter