Let P∈SylpG,ch(P) be any characteristic subgroup of P. A group C is called a Cp-group if G satisfies the condition 'NG(ch(P)) is p-nilpotent implies that G is p-nilpotent'. In this paper some properties on Gp...Let P∈SylpG,ch(P) be any characteristic subgroup of P. A group C is called a Cp-group if G satisfies the condition 'NG(ch(P)) is p-nilpotent implies that G is p-nilpotent'. In this paper some properties on Gp-groups and some suffcient conditions for a group to be p-nilpotent are obtained.展开更多
By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and sup...By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.展开更多
基金This research was supported by National Natural Scicnce Foundation of China and Foundation of Guangxi Education Committee
文摘Let P∈SylpG,ch(P) be any characteristic subgroup of P. A group C is called a Cp-group if G satisfies the condition 'NG(ch(P)) is p-nilpotent implies that G is p-nilpotent'. In this paper some properties on Gp-groups and some suffcient conditions for a group to be p-nilpotent are obtained.
文摘研究环的Ore扩张的幂零p.p.性,幂零Baer性和弱Mc Coy性,主要证明了:设R是一个拟IFP和(α,δ)-condition环,则有(1)如果R是幂零p.p.-环,则R[x;α,δ]是幂零p.p.-环;(2)如果R是幂零Baer环,则R[x;α,δ]是幂零Baer环;(3)R[x;α,δ]是右弱M c Coy环。
文摘By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.
