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1.
Michael Huber 《Journal of Combinatorial Theory, Series A》2010,117(2):196-203
This paper takes a significant step towards confirming a long-standing and far-reaching conjecture of Peter J. Cameron and Cheryl E. Praeger. They conjectured in 1993 that there are no non-trivial block-transitive 6-designs. We prove that the Cameron-Praeger conjecture is true for the important case of non-trivial Steiner 6-designs, i.e. for 6-(v,k,λ) designs with λ=1, except possibly when the group is PΓL(2,pe) with p=2 or 3, and e is an odd prime power. 相似文献
2.
Michael Huber 《Journal of Algebraic Combinatorics》2007,26(2):183-207
Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural
one. Consequently, in the last decades flag-transitive Steinert-designs (i.e. flag-transitive t-(v,k,1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been
possible in recent years to essentially characterize all flag-transitive Steiner 2-designs. However, despite the finite simple
group classification, for Steiner t-designs with parameters t > 2 such characterizations have remained challenging open problems for about 40 years (cf. [11, p. 147] and [12 p. 273],
but presumably dating back to around 1965). The object of the present paper is to give a complete classification of all flag-transitive
Steiner 4-designs. Our result relies on the classification of the finite doubly transitive permutation groups and is a continuation
of the author's work [20, 21] on the classification of all flag-transitive Steiner 3-designs.
2000 Mathematics Subject Classification. Primary 51E10 . Secondary 05B05 . 20B25 相似文献
3.
A recent paper of O'Reilly Regueiro obtained an explicit upper bound on the number of points of a flag-transitive, 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. 相似文献
4.
Zvonimir Janko 《组合设计杂志》1999,7(1):17-19
The existence of symmetric designs with parameters (105, 40, 15) was shown. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 17–19, 1999 相似文献
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Alice Devillers Michael Giudici Cai Heng Li Cheryl E. Praeger 《Journal of Combinatorial Theory, Series A》2013,120(7):1855-1870
The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case. 相似文献
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Mariusz Grech 《Discrete Mathematics》2010,310(21):2877-2882
We show that with the exception of four known cases: C3, C4, C5, and , all regular permutation groups can be represented as symmetric groups of boolean functions. This solves the problem posed by A. Kisielewicz in the paper [A. Kisielewicz, Symmetry groups of boolean functions and constructions of permutation groups, J. Algebra 199 (1998) 379-403]. A slight extension of our proof yields the same result for semiregular groups. 相似文献
11.
An incomplete t‐wise balanced design of index λ is a triple (X,H,??) where X is a υ–element set, H is a subset of X called the hole, and B is a collection of subsets of X called blocks, such that, every t‐element subset of X is either in H or in exactly λ blocks, but not both. If H is a hole in an incomplete t‐wise balanced design of order υ and index λ, then |H| ≤ υ/2 if t is odd and |H| ≤ (υ ? 1)/2 if t is even. In particular, this result establishes the validity of Kramer's conjecture that the maximal size of a block in a Steiner t‐wise balanced design is at most υ/2 if t is odd and at most (υ?1)/2 when t is even. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 269–284, 2001 相似文献
12.
U. Dempwolff 《Designs, Codes and Cryptography》2001,22(2):191-207
We determine the symmetric designs
which admit a group
such that G has a nonabelian socle and is a primitiverank 3 group on points (and blocks). 相似文献
13.
Daniil Shved 《代数通讯》2017,45(5):1842-1852
If G is an arbitrary group, then the group Autvt(G) consists, by definition, of all virtually trivial automorphisms of G, i.e. of all automorphisms that have the fixed-point subgroup of finite index in G. We investigate the structure of Autvt(G) and show that it possesses a certain “well-behaved” normal series which demonstrates its closeness to finitary linear groups. This is then used to prove that each simple section of Autvt(G) is a finitary linear group. 相似文献
14.
Laércio J. dosSantos 《Indagationes Mathematicae》2007,18(1):135-146
Let G be a Lie group and L C G a Lie subgroup. We give necessary and sufficient conditions for a family of cosets of L to generate a subsemigroup with nonempty interior in G. We apply these conditions to symmetric pairs (G, L) where L is a subgroup of G such that Go C L C Gi and r is an involutive automorphism of G. As a consequence we prove that for several r the fixed point group GI is a maximal semigroup. 相似文献
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Automorphisms of groups acting faithfully on rooted trees are studied. We find conditions under which every automorphism of such a group is induced by a conjugation from the full automorphism group of the rooted tree. These results are applied to known examples such as Grigorchuk groups, Gupta–Sidki group, etc. 相似文献
17.
Eric Merchant 《Journal of Algebraic Combinatorics》2006,24(2):137-155
Let n be the order of a Hadamard design, and G any finite group. Then there exists many non-isomorphic Hadamard designs of order 212|G| + 13
n with automorphism group isomorphic to G.This research was supported in part by the National Science Foundation. 相似文献
18.
In this article we give several results and problems on the permutation groups, having an interest for cryptography.
The abstract of the talk at the international conference Algebra and its applications (Krasnoyarsk, August 5–9, 2002).Mathematics Subject Classifications (2000) 05E20, 20B05, 20F05. 相似文献
19.
The problem of classifying cyclic Steiner quadruple systems (CSQSs) is considered. A computational approach shows that the number of isomorphism classes of such designs with orders 26 and 28 is 52,170 and 1,028,387, respectively. It is further shown that CSQSs of order 2p, where p is a prime, are isomorphic iff they are multiplier equivalent. Moreover, no CSQSs of order less than or equal to 38 are isomorphic but not multiplier equivalent. 相似文献
20.
Rajendra M. Pawale 《组合设计杂志》2007,15(1):49-60
The following results for proper quasi‐symmetric designs with non‐zero intersection numbers x,y and λ > 1 are proved.
- (1) Let D be a quasi‐symmetric design with z = y ? x and v ≥ 2k. If x ≥ 1 + z + z3 then λ < x + 1 + z + z3.
- (2) Let D be a quasi‐symmetric design with intersection numbers x, y and y ? x = 1. Then D is a design with parameters v = (1 + m) (2 + m)/2, b = (2 + m) (3 + m)/2, r = m + 3, k = m + 1, λ = 2, x = 1, y = 2 and m = 2,3,… or complement of one of these design or D is a design with parameters v = 5, b = 10, r = 6, k = 3, λ = 3, and x = 1, y = 2.
- (3) Let D be a triangle free quasi‐symmetric design with z = y ? x and v ≥ 2k, then x ≤ z + z2.
- (4) For fixed z ≥ 1 there exist finitely many triangle free quasi‐symmetric designs non‐zero intersection numbers x, y = x + z.
- (5) There do not exist triangle free quasi‐symmetric designs with non‐zero intersection numbers x, y = x + 2.