For an odd prime p = 7, let q be a power of p such that q3 ≡ 1 (mod 7). It is known that the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to PSL(2, 7). For such a projective group , we investigate the geometric properties of the (unique) -orbit of size 42 such that the 1-point stabilizer of in is a cyclic group of order 4. We present a computational approach to prove that is a 42-arc provided that q ≥ 53 and q = 373, 116, 56, 36. We discuss the case q = 53 in more detail showing the completeness of for q = 53.
42-arcs in PG(2, q) left invariant by PSL(2, 7)
KORCHMAROS, Gabor
2012-01-01
Abstract
For an odd prime p = 7, let q be a power of p such that q3 ≡ 1 (mod 7). It is known that the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to PSL(2, 7). For such a projective group , we investigate the geometric properties of the (unique) -orbit of size 42 such that the 1-point stabilizer of in is a cyclic group of order 4. We present a computational approach to prove that is a 42-arc provided that q ≥ 53 and q = 373, 116, 56, 36. We discuss the case q = 53 in more detail showing the completeness of for q = 53.File in questo prodotto:
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