Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）,...Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.展开更多
Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning t...Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C;（α;） and G/[G, α;] are both abelian-by-finite.展开更多
Recently,Makhnev and Nirova found intersection arrays of distance-regular graphs withλ=2 and at most 4096 vertices.In the case of primitive graphs of diameter 3 withμ=1 there corresponding arrays are{18,15,9;1,1,10}...Recently,Makhnev and Nirova found intersection arrays of distance-regular graphs withλ=2 and at most 4096 vertices.In the case of primitive graphs of diameter 3 withμ=1 there corresponding arrays are{18,15,9;1,1,10},{33,30,8;1,1,30}or{39,36,4;1,1,36}.In this work,possible orders and subgraphs of fixed points of the hypothetical distance-regular graph with intersection array{18,15,9;1,1,10}are studied.In particular,graph with intersection array{18,15,9;1,1,10}is not vertex symmetric.展开更多
Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG...Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG(a^p)and G/[G,a^p]are both nilpotent-by-finite.展开更多
Let A be a ring with indentity, G a finite group of automorphisms of A. The main result of this paper is that A/AG is Galois if and only if it is Frobenius and the module AGA (or AAG)is faithful. Moreover if |G| is in...Let A be a ring with indentity, G a finite group of automorphisms of A. The main result of this paper is that A/AG is Galois if and only if it is Frobenius and the module AGA (or AAG)is faithful. Moreover if |G| is invertible the author improves [2, Theorem 8] and [3, Theorem 8].展开更多
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.
基金Supported by National Natural Science Foundation of China(Grant No.11371124)Youth Foundation of Hebei Educational Committee(Grant Nos.QN2016184 and F2015402033)Graduate Education Teaching Reform Foundation of Hebei University of Engineering(Grant No.161290140004)
文摘Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C;（α;） and G/[G, α;] are both abelian-by-finite.
基金The work was performed under support of RSF,project 14-11-00061(Theorem 1.1)agreement between ministry of education and science of Russian Federation and the Ural federal university on 27.08.2013,No.02.A03.21.0006(Corollary 1.2).
文摘Recently,Makhnev and Nirova found intersection arrays of distance-regular graphs withλ=2 and at most 4096 vertices.In the case of primitive graphs of diameter 3 withμ=1 there corresponding arrays are{18,15,9;1,1,10},{33,30,8;1,1,30}or{39,36,4;1,1,36}.In this work,possible orders and subgraphs of fixed points of the hypothetical distance-regular graph with intersection array{18,15,9;1,1,10}are studied.In particular,graph with intersection array{18,15,9;1,1,10}is not vertex symmetric.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11801129,11771129)the Natural Science Foundation of Hebei Province(No.A2019402211)+3 种基金the Program for Young Top Talent of Higher Learning Institutions of Hebei(No.BJ2018025)the Foundation of Handan(No.1723208068-5)the Excellent Young and Middle-Aged Innovative Team Program of Hubei(No.T201601)the New Century High-Level Talents Foundation of Hubei.
文摘Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG(a^p)and G/[G,a^p]are both nilpotent-by-finite.
文摘Let A be a ring with indentity, G a finite group of automorphisms of A. The main result of this paper is that A/AG is Galois if and only if it is Frobenius and the module AGA (or AAG)is faithful. Moreover if |G| is invertible the author improves [2, Theorem 8] and [3, Theorem 8].
