Some constructions of divisible designs from Laguerre geometries

In the nineties, A.G. Spera introduced a construction principle for divisible designs. Using this method, we get series of divisible designs from finite Laguerre geometries. We show a close connection between some of these divisible designs and divisible designs whose construction was based on a conic in a plane of a three-dimensional projective space.     

On the first homology of automorphism groups of manifolds with geometric structures

Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category. This research was partially supported by Grant-in-Aid for Scientific Research (No. 16540058), Japan Society for the Promotion of Science. This research was partially supported by Grant-in-Aid for Scientific Research (No. 14540093), Japan Society for the Promotion of Science.     

A result on the weight distributions of binary quadratic residue codes

Truong et al. [7]proved that the weight distribution of a binary quadratic residue code C with length congruent to −1 modulo 8 can be determined by the weight distribution of a certain subcode of C containing only one-eighth of the codewords of C. In this paper, we prove that the same conclusion holds for any binary quadratic residue codes.     

4度对称循环图的分类(英文)

本文刻划了所有4度有向和无内循环图．     

|T |+‐resplendent models and the Lascar group

In this paper we show that in every |T |⁺‐resplendent model N , for every A ? N such that |A | ≤ |T |, the group Autf(N/A ) of strong automorphisms is the least very normal subgroup of the group Aut(N/A ) and the quotient Aut(N/A )/Autf(N/A ) is the Lascar group over A . Then we generalize this result to every |T |⁺‐saturated and strongly |T |⁺‐homogeneous model. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unifying some known infinite families of combinatorial 3-designs

In this paper we present a construction of 3-designs by using a 3-design with resolvability. The basic construction generalizes a well-known construction of simple 3-(v,4,3) designs by Jungnickel and Vanstone (1986). We investigate the conditions under which the designs obtained by the basic construction are simple. Many infinite families of simple 3-designs are presented, which are closely related to some known families by Iwasaki and Meixner (1995), Laue (2004) and van Tran (2000, 2001). On the other hand, the designs obtained by the basic construction possess various properties: A theory of constructing simple cyclic 3-(v,4,3) designs by Köhler (1981) can be readily rebuilt from the context of this paper. Moreover many infinite families of simple resolvable 3-designs are presented in comparison with some known families. We also show that for any prime power q and any odd integer n there exists a resolvable 3-(qn+1,q+1,1) design. As far as the authors know, this is the first and the only known infinite family of resolvable t-(v,k,1) designs with t?3 and k?5. Those resolvable designs can again be used to obtain more infinite families of simple 3-designs through the basic construction.     

广义超特殊p-群的自同构群Ⅲ

确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|■G|=p~m,其中n≥1,m≥2,Aut_fG是AutG中平凡地作用在Frat G上的元素形成的正规子群,则(1)当G的幂指数是p~m时,(i)如果p是奇素数,那么AutG/AutfG≌Z_((p-1)p~(m-2)),并且AutfG/InnG≌Sp(2n,p)×Zp.(ii)如果p=2,那么AutG=Aut_fG(若m=2)或者AutG/AutfG≌Z_(2~(m-3))×Z_2(若m≥3),并且AutfG/InnG≌Sp(2n,2)×Z_2.(2)当G的幂指数是p~(m+1)时,(i)如果p是奇素数,那么AutG=〈θ〉■Aut_fG,其中θ的阶是(p-1)p~(m-1),且Aut_f G/Inn G≌K■Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群.(ii)如果p=2,那么AutG=〈θ_1,θ_2〉■Aut_fG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2~(m-2))×Z_2,并且Aut_fG/Inn G≌K×Sp(2n-2,2),其中K是2~(2n-1)阶初等Abel 2-群.特别地,当n=1时...     

Generalized Skew Derivations with Nilpotent Values in Prime Rings

Let ? be a prime ring, 𝒞 the extended centroid of ?, ? a Lie ideal of ?, F be a nonzero generalized skew derivation of ? with associated automorphism α, and n ≥ 1 be a fixed integer. If (F(xy) ? yx) ⁿ  = 0 for all x, y ∈ ?, then ? is commutative and one of the following statements holds:

(1) Either ? is central;

(2) Or ? ? M ₂(𝒞), the 2 × 2 matrix ring over 𝒞, with char(𝒞) = 2.     

Automorphism Groups of Finite Abelian p-groups and Transvections

We define a particular type of automorphisms called transvections on a finite finite abelian p-group H_p. It is proved that the subgroup E of the automorphism group Aut(H_p) of H_p generated by those transvections is normal in it, and that Aut(H_p) can be written as the product of E and some abelian subgroup K. The center of Aut(H_p) is also determined.