Book Review
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MathSciNet review:
1567306
Full text of review:
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Book Information:
Author:
Heinz Lüneburg
Title:
Translation planes
Additional book information:
Springer-Verlag, Berlin and New York, 1980, ix + 278 pp., $29.80.
P. Dembowski, Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Springer-Verlag, Berlin-New York, 1968. MR 0233275
David A. Foulser, Replaceable translation nets, Proc. London Math. Soc. (3) 22 (1971), 235–264. MR 291935, DOI 10.1112/plms/s3-22.2.235
Christoph Hering, A new class of quasifields, Math. Z. 118 (1971), 56–57. MR 285415, DOI 10.1007/BF01109894
Christoph Hering, On shears of translation planes, Abh. Math. Sem. Univ. Hamburg 37 (1972), 258–268. MR 305223, DOI 10.1007/BF02999703
Daniel R. Hughes and Fred C. Piper, Projective planes, Graduate Texts in Mathematics, Vol. 6, Springer-Verlag, New York-Berlin, 1973. MR 0333959
Michael J. Kallaher, On finite affine planes of rank $3$, J. Algebra 13 (1969), 544–553. MR 247567, DOI 10.1016/0021-8693(69)90116-1
Michael J. Kallaher, A survey of weak rank $3$ affine planes, Proceedings of the International Conference Projective Planes (Washington State Univ., Pullman, Wash., 1973) Washington State Univ. Press, Pullman, Wash., 1973, pp. 121–143. MR 0362035
M. J. Kallaher and T. G. Ostrom, Collineation groups irreducible on the components of a translation plane, Geom. Dedicata 9 (1980), no. 2, 153–194. MR 578195, DOI 10.1007/BF00147435
Robert A. Liebler, Finite affine planes of rank three are translation planes, Math. Z. 116 (1970), 89–93. MR 266039, DOI 10.1007/BF01109955
Robert A. Liebler, On finite line transitive affine planes of rank $3$, Proceedings of the International Conference on Projective Planes (Washington State Univ., Pullman, Wash., 1973) Washington State Univ. Press, Pullman, Wash., 1973, pp. 165–179. MR 0362036
T. G. Ostrom, Linear transformations and collineations of translation planes, J. Algebra 14 (1970), 405–416. MR 261436, DOI 10.1016/0021-8693(70)90114-6
T. G. Ostrom, Finite translation planes, Lecture Notes in Mathematics, Vol. 158, Springer-Verlag, Berlin-New York, 1970. MR 0275274
T. G. Ostrom, Classification of finite translation planes, Proceedings of the International Conference on Projective Planes (Washington State Univ., Pullman, Wash., 1973) Washington State Univ. Press, Pullman, Wash., 1973, pp. 195–213. MR 0362039
T. G. Ostrom, Recent advances in finite translation planes, Foundations of geometry (Proc. Conf., Univ. Toronto, Toronto, Ont., 1974) Univ. Toronto Press, Toronto, Ont., 1976, pp. 183–205. MR 0400042
T. G. Ostrom, Finite translation planes, an exposition, Aequationes Math. 15 (1977), no. 2-3, 121–133. MR 461262, DOI 10.1007/BF01835642
Udo Ott, Eine neue Klasse endlicher Translationsebenen, Math. Z. 143 (1975), no. 2, 181–185 (German). MR 388237, DOI 10.1007/BF01187061
Günter Pickert, Projektive Ebenen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXX, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0073211
Asher Wagner, On finite affine line transitive planes, Math. Z. 87 (1965), 1–11. MR 172165, DOI 10.1007/BF01109922
- 1.
- P. Dembowski, Finite geometries, Springer-Verlag, Berlin and New York, 1968. MR 0233275
- 2.
- D. Foulser, Replaceable translation nets, Proc. London Math. Soc. 22 (1971), 235-264. MR 291935
- 3.
- C. Hering, A new class of quasifields, Math. Z. 118 (1970), 56-57. MR 285415
- 4.
- C. Hering, On shears of translation planes, Abh. Math. Sem. Ham. 37 (1972), 258-268. MR 305223
- 5.
- D. R. Hughes and F. C. Piper, Projective planes, Springer-Verlag, Berlin and New York, 1973. MR 333959
- 6.
- M. J. Kallaher, On finite affine planes of rank 3, J. Algebra 13 (1969), 544-553. MR 247567
- 7.
- M. J. Kallaher, A survey of weak rank 2 affine planes, Proc. Internat. Conf. on Projecture Planes, (M. J. Kallaher and T. G. Ostrom (eds.)), Wash. St. Univ. Press, Pullman, Washington, 1973. MR 362035
- 8.
- M. J. Kallaher and T. G. Ostrom, Collineation groups irreducible on the components of a translation plane, Geom. Dedicata 9 (1980), 153-194. MR 578195
- 9.
- R. A. Liebler, Finite affine planes of rank three are translation planes, Math. Z. 116 (1970), 89-93. MR 266039
- 10.
- R. A. Liebler, On finite line transitive affine planes of rank 3, Proc. Internat. Conf. on projective Planes, Wash. St. Univ. Press, Pullman, Washington, 1973. MR 362036
- 11.
- T. G. Ostrom, Linear transformations and collineations of translation planes, J. Algebra 14 (1970), 405-416. MR 261436
- 12.
- T. G. Ostrom, Finite translation planes, Lecture Notes in Math., vol. 158, Springer-Verlag, Berlin and New York, 1970. MR 275274
- 13.
- T. G. Ostrom, Classification of finite translation planes, Proc. Internat. Conf. on Projective Planes, Wash. St. Univ. Press, Pullman, Washington, 1970. MR 362039
- 14.
- T. G. Ostrom, Recent advances in finite translation planes, Foundations of Geometry, (P. Scherk (ed.)), Univ. Toronto Press, Toronto, Canada, 1976. MR 400042
- 15.
- T. G. Ostrom, Finite translation planes, an exposition, Aequationes Math. 15 (1977), 121-133. MR 461262
- 16.
- U. Ott, Über eine neue Klasse endlicher Translationsebene, Math. Z. 143 (1975), 181-185. MR 388237
- 17.
- G. Pickert, Projektive Ebenen, Springer-Verlag, Berlin and New York, 1955. MR 73211
- 18.
- A. Wagner, On finite affine line transitive planes, Math. Z. 87 (1965), 1-11. MR 172165
Review Information:
Reviewer:
T. G. Ostrom
Journal:
Bull. Amer. Math. Soc.
4 (1981), 215-218
DOI:
https://doi.org/10.1090/S0273-0979-1981-14889-8
