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 finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commutin...Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.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The NSF(11301150,11371124)of Chinathe NSF(142300410134)of Henan ProvincePlan for Scientific Innovation Talent(11CXRC19)of Henan University of Technology
文摘Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.
