A survey of the automorphism groups of block designs

Camina, A. R.

doi:10.1002/jcd.3180020205

Cited by 23 publications

(18 citation statements)

References 80 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly (v − f ) mod p = 0 and f ≤ v/2, see[5]. Tonchev (Lemma 1.8.1[27]) proved that an automorphism of order 3 of a 2-(v,k,λ) design fixes at most b − 3(r − λ) blocks.…”

mentioning

confidence: 99%

2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order, and their related Hadamard matrices and codes

Bouyukliev

Fack

Winne

2008

Des. Codes Cryptogr.

View full text Add to dashboard Cite

We present the full classification of Hadamard 2-(31,15,7), Hadamard 2-(35, 17,8) and Menon 2-(36,15,6) designs with automorphisms of odd prime order. We also give partial classifications of such designs with automorphisms of order 2. These classifications lead to related Hadamard matrices and self-dual codes. We found 76166 Hadamard matrices of order 32 and 38332 Hadamard matrices of order 36, arising from the classified designs. Remarkably, all constructed Hadamard matrices of order 36 are Hadamard equivalent to a regular Hadamard matrix. From our constructed designs, we obtained 37352 doubly-even [72,36,12] codes, which are the best known self-dual codes of this length until now

show abstract

“…Clearly (v − f ) mod p = 0 and f ≤ v/2, see[5]. Tonchev (Lemma 1.8.1[27]) proved that an automorphism of order 3 of a 2-(v,k,λ) design fixes at most b − 3(r − λ) blocks.…”

mentioning

confidence: 99%

2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order, and their related Hadamard matrices and codes

Bouyukliev

Fack

Winne

2008

Des. Codes Cryptogr.

View full text Add to dashboard Cite

show abstract

“…Table 3 C o l u m n 1 2 3 4 5 6 7 8 9 1 0 k 11 15 16 20 21 25 26 30 31 35 v 12 22 25 39 43 61 66 88 94 120 If λ = 9, then 10 k 27, and (3) implies that (k, v) = (10, 11), (18,35), (19,39), or (27, 79); but since v k + 2 and v is not prime, only the second and third pairs are allowed (and D is an Hadamard design or a complement of an Hadamard design). If k = 19, then (4) implies that v = c and we have a contradiction. Hence (k, v) = (18, 35).…”

Section: Proof Letmentioning

confidence: 78%

“…However (4) implies that 17 divides c − 1, which is impossible for any proper divisor of 35. Table 3 C o l u m n 1 2 3 4 5 6 7 8 9 1 0 k 11 15 16 20 21 25 26 30 31 35 v 12 22 25 39 43 61 66 88 94 120 If λ = 9, then 10 k 27, and (3) implies that (k, v) = (10, 11), (18,35), (19,39), or (27, 79); but since v k + 2 and v is not prime, only the second and third pairs are allowed (and D is an Hadamard design or a complement of an Hadamard design).…”

Section: Proof Letmentioning

confidence: 96%

See 1 more Smart Citation

Imprimitive flag-transitive symmetric designs

Praeger

Zhou

2006

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

A recent paper of O'Reilly Regueiro obtained an explicit upper bound on the number of points of a flagtransitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of these parameter sequences.

show abstract

“…The papers [7] and [17] contain discussions of the automorphism groups of these spaces. Also two recent surveys of work in this area can be found in [4] and [12].…”

Section: Introductionmentioning

confidence: 99%

Line-transitive, point quasiprimitive automorphism groups of finite linear spaces are affine or almost simple

Camina

Praeger

2001

Aequationes Mathematicae

Self Cite

View full text Add to dashboard Cite

The paper reports on an investigation of the structure of line-transitive automorphism groups of a finite linear space. It follows from a result of Richard Block that such a group G is also point-transitive. It has been proved by several people independently that, if in addition G is transitive on flags (incident point-line pairs), then G acts primitively on points and is either an almost simple group or a group of affine transformations of a finite vector space. Recently the first author proved that the conclusion that G is almost simple or affine holds under the weaker assumptions that G is line-transitive and point-primitive. We strengthen this result, proving that G is almost simple or affine under the (even weaker) assumptions that G is linetransitive and point-quasiprimitive. (A permutation group is quasiprimitive if every nontrivial normal subgroup is transitive.) This result is best possible since several examples are known of line-transitive automorphism groups G which are not quasiprimitive on points, and are neither almost simple nor affine. Mathematics Subject Classification (2000). 20B25, 05B05.

show abstract

A survey of the automorphism groups of block designs

Cited by 23 publications

References 80 publications

2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order, and their related Hadamard matrices and codes

2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order, and their related Hadamard matrices and codes

Imprimitive flag-transitive symmetric designs

Line-transitive, point quasiprimitive automorphism groups of finite linear spaces are affine or almost simple

Contact Info

Product

Resources

About