Autotopism groups of cyclic semifield planes
Ulrich Dempwolff
DOI: 10.1007/s10801-011-0286-4
Abstract
In this article we investigate the autotopism group of the so-called cyclic semifield planes. We show that the group generated by the homology groups of the nuclei is already the full group of autotopisms that are linear with respect to the nuclei. The full autotopism group is also computed with the exception of one special subcase.
Pages: 641–669
Keywords: keywords semifield; autotopism group; finite plane
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References
1. Aschbacher, M.: Finite Group Theory, 2nd edn., Cambridge Univ. Press, Cambridge (2000)
2. Bell, G.: Cohomology of degree 0, 1 and 2 of SLn(q) I-II. J. Algebra 54, 216-238, 239-259 (1978)
3. Dembowski, P.: Finite Geometries. Springer, Berlin (1968)
4. Dempwolff, U.: On irreducible semilinear transformations. Forum Math. 22, 1193-1206 (2010)
5. Hughes, D., Piper, F.: Projective Planes. Springer, Berlin (1973)
6. Jha, V., Johnson, N.: An analog of the Albert-Knuth theorem on the orders of finite semifields and a complete solution to Cofman's subplane problem. Algebras Groups Geom. 6, 1-35 (1989)
7. Johnson, N., Marino, G., Polverino, O., Trombetti, R.: On a generalization of cyclic semifields. J. Al- gebr. Comb. 29, 1-34 (2009)
8. Kantor, W.: Finite semifields. In: Hulpke, A., Liebler, R., Penttila, T., Seress, A. (eds.) Finite Geometries, Groups, and Computation, pp. 103-114. Pingree Park Col., USA, Sept. 4-9 2004. de Gruyter, Berlin (2006)
9. Kantor, W., Liebler, R.: Semifields arising from irreducible semilinear transformations. J. Aust. Math.
2. Bell, G.: Cohomology of degree 0, 1 and 2 of SLn(q) I-II. J. Algebra 54, 216-238, 239-259 (1978)
3. Dembowski, P.: Finite Geometries. Springer, Berlin (1968)
4. Dempwolff, U.: On irreducible semilinear transformations. Forum Math. 22, 1193-1206 (2010)
5. Hughes, D., Piper, F.: Projective Planes. Springer, Berlin (1973)
6. Jha, V., Johnson, N.: An analog of the Albert-Knuth theorem on the orders of finite semifields and a complete solution to Cofman's subplane problem. Algebras Groups Geom. 6, 1-35 (1989)
7. Johnson, N., Marino, G., Polverino, O., Trombetti, R.: On a generalization of cyclic semifields. J. Al- gebr. Comb. 29, 1-34 (2009)
8. Kantor, W.: Finite semifields. In: Hulpke, A., Liebler, R., Penttila, T., Seress, A. (eds.) Finite Geometries, Groups, and Computation, pp. 103-114. Pingree Park Col., USA, Sept. 4-9 2004. de Gruyter, Berlin (2006)
9. Kantor, W., Liebler, R.: Semifields arising from irreducible semilinear transformations. J. Aust. Math.
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