ISSN:0024-6093    

DOI:10.1112/blms/22.6.529

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

By using some finite local rings, we construct some new partial difference sets and relative difference sets onpgroups wherepis any prime. Whenp= 2, some of partial difference sets constructed are reversible difference sets which include Dillon's difference sets.

ISSN:0024-6093    

DOI:10.1112/blms/22.6.533

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6093    

DOI:10.1112/blms/22.6.540

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this paper we show how to associate to any real projective algebraic varietyZ⊂RPn−1a real polynomialF1:Rn,0 →R, 0 with an algebraically isolated singularity, having the property that χ(Z) = ½(1 − deg (gradF1), where deg (gradF1is the local real degree of the gradient gradF1:Rn, 0 →Rn, 0. This degree can be computed algebraically by the method of Eisenbud and Levine, and Khimshiashvili [5]. The varietyZneed not be smooth.This leads to an expression for the Euler characteristic of any compact algebraic subset ofRn, and the link of a quasihomogeneous mappingf:Rn, 0 →Rn, 0 again in terms of the local degree of a gradient with algebraically isolated singularity.Similar expressions for the Euler characteristic of an arbitrary algebraic subset ofRnand the link of any polynomial map are given in terms of the degrees of algebraically finite gradient maps. These maps do involve ‘sufficiently small’ constants, but the degrees involved ar (theoretically, at least) algebraically computable.

ISSN:0024-6093    

DOI:10.1112/blms/22.6.547

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A cubic (trivalent) graph Γ is said to be 4‐arc‐transitive if its automorphism group acts transitively on the 4‐arcs of Γ (where a 4‐arc is a sequencev0,v1, …v4of vertices of Γ such thatvi−1is adjacent tovifor 1 ⩽i⩽ 4, andvi−1≠vi+1for 1 ⩽i<4). In his investigations into graphs of this sort, Biggs defined a family of groups 4+(am), form= 3,4,5…, each presented in terms of generators and relations under the additional assumption that the vertices of a circuit of lengthmare cyclically permuted by some automorphism. In this paper it is shown that whenevermis a proper multiple of 6, the group 4+(am) is infinite. The proof is obtained by constructing transitive permutation representations of arbitrarily large degree.

ISSN:0024-6093    

DOI:10.1112/blms/22.6.553

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6093    

DOI:10.1112/blms/22.6.561

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

LetGbe a finite group. Attach toGthe following graph Γ: its vertices are the non‐central conjugacy classes ofG, and two vertices are connected if their cardinalities arenotcoprime. Denote byn(Γ) the number of the connecte components of Γ. We prove thatn(Γ) ⩽ 2 for all finite groups, and we completely characterize groups withn(Γ) = 2. When Γ is connected, then the diameter of the graph is at most 4. For simple non‐abelian finite groups, the graph is complete. Similar results are proved for infinite FC‐groups.

ISSN:0024-6093    

DOI:10.1112/blms/22.6.569

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6093    

DOI:10.1112/blms/22.6.576

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6093    

DOI:10.1112/blms/22.6.583

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6093    

DOI:10.1112/blms/22.6.591

出版商:Oxford University Press    

年代:2016

数据来源: WILEY