Nuclear fusion in finite semifield planes
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| 024 | 7 | 0 | |a 10.1515/advg.2004.4.4.413 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/advg.2004.4.4.413 | ||
| 245 | 0 | 0 | |a Nuclear fusion in finite semifield planes |h [Elektronische Daten] |c [Vikram Jha, Norman L. Johnson] |
| 520 | 3 | |a 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. | |
| 540 | |a © de Gruyter | ||
| 690 | 7 | |a Geometry |2 nationallicence | |
| 700 | 1 | |a Jha |D Vikram |4 aut | |
| 700 | 1 | |a Johnson |D Norman L. |4 aut | |
| 773 | 0 | |t Advances in Geometry |d Walter de Gruyter |g 4/4(2004-11-03), 413-432 |x 1615-715X |q 4:4<413 |1 2004 |2 4 |o advg | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/advg.2004.4.4.413 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/advg.2004.4.4.413 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Jha |D Vikram |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Johnson |D Norman L. |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Advances in Geometry |d Walter de Gruyter |g 4/4(2004-11-03), 413-432 |x 1615-715X |q 4:4<413 |1 2004 |2 4 |o advg | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||