In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Fi...In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.展开更多
For a positive integer n,we denote byπ(n)the set of all prime divisors of n.For a finite group G,the setπ(G):=π(|G|)is called the prime spectrum of G.Let M<G mean that M is a maximal subgroup of G.We put K(G)=ma...For a positive integer n,we denote byπ(n)the set of all prime divisors of n.For a finite group G,the setπ(G):=π(|G|)is called the prime spectrum of G.Let M<G mean that M is a maximal subgroup of G.We put K(G)=max{|π(G)\π(M)|:M<G}and k(G)=min{|π(G)\π(M)|:M<G}.In this notice,using well-known number-theoretical results,we present a number of examples to show that both K(G)and k(G)are unbounded in general.This implies that the problem"Are k(G)and K(G)bounded by some constant k?",raised by Monakhov and Skiba in 2016,is solved in the negative.展开更多
文摘In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.
文摘For a positive integer n,we denote byπ(n)the set of all prime divisors of n.For a finite group G,the setπ(G):=π(|G|)is called the prime spectrum of G.Let M<G mean that M is a maximal subgroup of G.We put K(G)=max{|π(G)\π(M)|:M<G}and k(G)=min{|π(G)\π(M)|:M<G}.In this notice,using well-known number-theoretical results,we present a number of examples to show that both K(G)and k(G)are unbounded in general.This implies that the problem"Are k(G)and K(G)bounded by some constant k?",raised by Monakhov and Skiba in 2016,is solved in the negative.
基金This research was supported by the National Natural Science Foundation of China(10771095)the Guangxi Science Foundation(0575052,0640070,0832107)+1 种基金the Innovation Project of Guangxi Graduate Education(2007106030701 M15)the Scientifc Research Foundation of Guangxi Educational Committee(200707LX233).
