Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩H^(g)=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G suc...Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩H^(g)=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.Furthermore,K is called K-P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that either K_(i-1)is normal in Ki or|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.In this paper,some properties of a nite group in which some particular subgroups are TI-subgroups or P-subnormal subgroups or K-P-subnormal subgroups are given.展开更多
文摘Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩H^(g)=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.Furthermore,K is called K-P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that either K_(i-1)is normal in Ki or|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.In this paper,some properties of a nite group in which some particular subgroups are TI-subgroups or P-subnormal subgroups or K-P-subnormal subgroups are given.
