Geodesic
On Translation Planes with Affine Central Collineations, II
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 116-129

Voir la notice de l'article provenant de la source Cambridge University Press

This article, as the name implies, is a continuation of [9]. In that article the second author investigates finite translation planes containing both affine dations and affine homologies. (See the beginning of Section 2 for definitions.) Such translation planes are called Ei7-planes. In [9] the author restricted himself to translation planes of characteristic p ≧ 5. The main reasons for this were that Ostrom's and Hering's theorem [13;4] on affine dations excluded the case p = 3 and the conclusions were easier to interpret geometrically when p ≧ 5 (as opposed to the case p = 2). Since then Ostrom [17] has settled the case p = 3. 
Johnson, Norman L.; Kallaher, Michael J. On Translation Planes with Affine Central Collineations, II. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 116-129. doi: 10.4153/CJM-1976-014-8
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[1] 1. André, J., Ûber nicht-Desarguessche Ebenen mit transitiver Translationgruppe, Math. Z. 60 (1954) 156–186. Google Scholar

[2] 2. Burmeister, M. V. D. and Hughes, D. R., On the solvability of autotopism groups, Arch. Math. 16 (1965), 178–183. Google Scholar

[3] 3. Dembowski, P., Finite geometries (Springer-Verlag, Berlin-Heidelberg, 1968). Google Scholar

[4] 4. Hering, C., On shears of translation planes, Abh. Math. Sem. Univ., Hamburg, 37 (1972), 258–268. Google Scholar

[5] 5. Hering, C., On projective planes of type VI, to appear. Google Scholar

[6] 6. Hua, L. K., On the automorphisms of the symplectic group over any field, Ann. of Math. 49 (1948), 739–759. Google Scholar

[7] 7. Hughes, D. R. and Piper, F. C., Projective planes (Springer-Verlag, New York-Heidelberg- Berlin, 1973). Google Scholar

[8] 8. Johnson, N. L. and Ostrom, T. G., Translation planes with several homology or elation groups of order 3, Geometriae Dedicata 2 (1973), 65–81. Google Scholar

[9] 9. Kallaher, M. J., On translation planes with affine central collineations, to appear in Geometriae Dedicata 4 (1975), 71–90. Google Scholar

[10] 10. Kallaher, M.J. and Ostrom, T. G., Fixed point free groups, rank three planes, and Bol quasifields, J. Algebra 18 (1971), 159–178. Google Scholar

[11] 11. Luneburg, H., Charakterisierungen der endlichen desarguesschen projektiven Ebenen, Math. Z. 85 (1964), 419–450. Google Scholar

[12] 12. Luneburg, H., Die Suzukigruppen und ihre geometrien, Lecture Notes in Mathematics (Springer-Verlag, Berlin-Heidelberg-New York, 1965). Google Scholar

[13] 13. Ostrom, T. G., Linear transformations and collineations of translation planes, J. Algebra 14 (1970), 405–416. Google Scholar

[14] 14. Ostrom, T. G., A class of translation planes admitting elations which are not translations, Arch. Math, 21 (1970), 214–217. Google Scholar

[15] 15. Ostrom, T. G., Finite translation planes, Lecture Notes in Mathematics (Springer-Verlag, Berlin- Heidelberg, 1970). Google Scholar

[16] 16. Ostrom, T. G., Homologies in translation planes, Proc. London Math. Soc. 26 (1973), 605–629. Google Scholar

[17] 17. Ostrom, T. G., Elations infinite translation planes of characteristic 3, Abh. Math. Sem. Hamb. 41 (1974), 179–184. Google Scholar

[18] 18. Suzuki, M., On a class of doubly transitive groups, Ann. Math. 75 (1962), 105–145. Google Scholar

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