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Lenz-Barlotti I.4 perspectivity groups are abelian
Author(s):
Robert
A.
Liebler;
Elizabeth
Scott-Janda
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1447-1451.
MSC (2000):
Primary 51-00, 05-00
Posted:
December 10, 2009
MathSciNet review:
2578538
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Abstract:
We extend a 1972 result of Kantor and Pankin and give a new elementary proof of the assertion in the title for projective planes of arbitrary order. The main tool appears in the very first book on group theory by Jordan in 1870.
References:
-
- 1.
- D. Ghinelli and D. Jungnickel: On finite projective planes in Lenz-Barlotti class at least I.3. Advances in Geometry 2003, suppl., S28-S48. MR 2028386 (2005a:51011)
- 2.
- M. Hall: The Theory of Groups, Macmillan, New York, 1959. MR 0103215 (21:1996)
- 3.
- D.R. Hughes: Partial difference sets. Amer. J. Math. 78 (1956), 650-674. MR 0084785 (18:921b)
- 4.
- C. Jordan: Traité des substitutions et des équations algébriques. Gauthiers-Villars, Paris, 1870.
- 5.
- W.M. Kantor: Projective planes of type I-4. Geometrica Ded. 3 (1974), 335-346. MR 0383233 (52:4114)
- 6.
- W.M. Kantor and M.D. Pankin: Commutativity in finite planes of type I-4. Arch. Math. (Basel) 23 (1972), 544-547. MR 0320883 (47:9416)
- 7.
- H. Naumann, Stufen der Begründung der ebenen affinen Geometrie. Math. Zeit. 60 (1954), 120-141. MR 0063058 (16:64c)
- 8.
- H. Wielandt: Finite Permutation Groups, Academic Press, New York, 1964. MR 0183775 (32:1252)
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Additional Information:
Robert
A.
Liebler
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Elizabeth
Scott-Janda
Affiliation:
Department of Mathematics, Armstrong Atlantic State University, Savannah, Georgia 31419
Address at time of publication:
3063 West Chapman Avenue, Orange, California 92868
DOI:
10.1090/S0002-9939-09-10051-5
PII:
S 0002-9939(09)10051-5
Received by editor(s):
July 30, 2008,
Received by editor(s) in revised form:
April 28, 2009
Posted:
December 10, 2009
Communicated by:
Jonathan I. Hall
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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