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On the automorphism group of planes of Figueroa type. (English) Zbl 0583.51003

Ch. Hering and H.-J. Schaeffer generalized R. Figueroa’s construction of finite projective planes. Their process yields also infinite projective planes. They determined the group of automorphisms of finite planes of Figueroa type.
The author of the present paper shows that the automorphism group of an infinite plane of Figueroa type is isomorphic to a direct product of a cyclic group of order 3 and \(P\Gamma\) L(3,F), where F is a field.
Reviewer: E.Ellers

MSC:

51A35 Non-Desarguesian affine and projective planes
51A10 Homomorphism, automorphism and dualities in linear incidence geometry
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References:

[1] U. Dempwolff , A note on the Figueroa planes; 43 ( 1984 ), 285-289. Arch. Math. MR 766437 | Zbl 0532.51009 · Zbl 0532.51009 · doi:10.1007/BF01247576
[2] R. Figueroa , A family of not (V, l)-transitive projective planes of order q3, q \? 1 (mod 3) and q > 2 ; Math. Z. , 181 ( 1982 ), pp. 471 - 479 . Article | Zbl 0477.51009 · Zbl 0477.51009 · doi:10.1007/BF01182385
[3] C. Hering - H.-J. SCHAEFFER, On the new projective planes of R. Figueroa, Combinatorial theory , Lecture notes Math ., no. 969 , Springer , Berlin ( 1982 ), pp. 187 - 190 . MR 692241 | Zbl 0498.51009 · Zbl 0498.51009
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