2021
DOI: 10.1016/j.jcta.2020.105309
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On flag-transitive 2-(v,k,2) designs

Abstract: The automorphism group of a flag-transitive 6-(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3-homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6-(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6-(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphi… Show more

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Cited by 18 publications
(28 citation statements)
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“…Lemma 5(vi) yields | k c c 16 ( − 1) which is satisfied in each remaining case. Combining Lemma 5(iii) and (v) yields d c = By Lemma 5(iii) r c = 4( − 1).Thus the possibilities for ℓ c d k r ( , , , , ) are(6,16,20,20,2),(10, 28, 32, 36,2), (26, 76, 80, 100, 2). (iv) ℓ x ( , ) = (3, 1).…”
mentioning
confidence: 87%
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“…Lemma 5(vi) yields | k c c 16 ( − 1) which is satisfied in each remaining case. Combining Lemma 5(iii) and (v) yields d c = By Lemma 5(iii) r c = 4( − 1).Thus the possibilities for ℓ c d k r ( , , , , ) are(6,16,20,20,2),(10, 28, 32, 36,2), (26, 76, 80, 100, 2). (iv) ℓ x ( , ) = (3, 1).…”
mentioning
confidence: 87%
“…For λ = 2 the bound in Proposition 7 gives ⩽ k 24. Together with Liang and Xia, the authors showed in [10] that there are only two imprimitive flag-transitive 2-designs, both of which are 2 − (16, 6, 2) designs. Thus this bound is definitely not tight for all λ.…”
Section: Proving (X) □mentioning
confidence: 99%
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“…Therefore, we correct Theorem 1.1 in [2] as below: Theorem 1.1 Let D be a nontrivial 2-design with gcd(r , λ) = 1, and let α be a point of D. Suppose that G is an automorphism group of D whose socle is X = PSU(n, q) with (n, q) = (3, 2). If G is flag-transitive, then λ ∈ {1, 2, 3, 5} and v, k, λ, X α and X are as in one of the lines in Table 1 or one of the following holds: It is worth noting by [6] that there is a general construction method for 2-designs from linear space:…”
Section: Introductionmentioning
confidence: 99%