Flag transitive geometries with trialities and no dualities coming from Suzuki groups
arxiv(2023)
摘要
Recently, Leemans and Stokes constructed an infinite family of incidence
geometries admitting trialities but no dualities from the groups PSL(2,q)
(where $q=p^{3n}$ with $p$ a prime and $n>0$ a positive integer). Unfortunately
these geometries are not flag transitive. In this paper, we construct the first
infinite family of incidence geometries of rank three that are flag transitive
and have trialities but no dualities. These geometries are constructed using
chamber systems of Suzuki groups Sz(q) (where $q=2^{2e+1}$ with $e$ a positive
integer and $2e+1$ is divisible by 3) and the trialities come from field
automorphisms. We also construct an infinite family of regular hypermaps with
automorphism group Sz(q) that admit trialities but no dualities.
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