8-Dimensional Compact Planes with an Automorphism Group which has a Normal Vector Subgroup

H. Salzmann

doi:10.5802/jolt.778

H. Salzmann

Journal of Lie Theory, Volume 24 (2014) no. 1, pp. 123-146

Abstract

A connected group Δ of automorphisms of an 8-dimensional compact plane P fixes at most some collinear points or 2 points and 2 lines (double flag). For each possible configuration of fixed elements of a group of sufficiently large dimension the structure of Δ and its action on P is determined. Examples are given; in the case of a double flag, all planes are described explicitly.

Zbl

DOI: 10.5802/jolt.778

Classification: 51H10
Keywords: Compact projective plane, Lie collineation group, elation, straight, dimension

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     author = {H. Salzmann},
     title = {8-Dimensional {Compact} {Planes} with an {Automorphism} {Group} which has a {Normal} {Vector} {Subgroup}},
     journal = {Journal of Lie Theory},
     pages = {123--146},
     year = {2014},
     volume = {24},
     number = {1},
     doi = {10.5802/jolt.778},
     zbl = {1296.51015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.778/}
}

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H. Salzmann. 8-Dimensional Compact Planes with an Automorphism Group which has a Normal Vector Subgroup. Journal of Lie Theory, Volume 24 (2014) no. 1, pp. 123-146. doi: 10.5802/jolt.778

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