On finite groups with given ICΦ-subgroups

被引:1
|
作者
Kaspczyk, Julian [1 ]
机构
[1] Tech Univ Dresden, Inst Algebra, D-01069 Dresden, Germany
关键词
Finite groups; IC Phi-subgroups; abelian; 2-nilpotent; nilpotent; solvably saturated formations; maximal subgroups; 2-maximal subgroups; 3-maximal subgroups; N-MAXIMAL SUBGROUPS;
D O I
10.1142/S0219498824500166
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A subgroup H of a group G is said to be an IC Phi-subgroup of G if H boolean AND [H,G] <= Phi(H). We analyze the structure of a finite group G under the assumption that some given subgroups of G are IC Phi-subgroups of G. A new characterization of finite abelian groups and some new criteria for 2-nilpotence and nilpotence of finite groups will be obtained. Moreover, we will obtain two criteria for a finite group to lie in a given solvably saturated formation containing the class of finite supersolvable groups.
引用
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页数:13
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