Minimal inner-Σ-Ω-groups and their applications

Abstract

We introduce and study the minimal inner-Σ-Ω-groups and the minimal outer-Σ--groups. Then we give some applications and obtain some interesting results, including characterizations of nilpotent, supersolvable, solvable, and p-closed groups in terms of the join of two conjugate cyclic subgroups having the same property. Keywordsnilpotent subgroup, supersolvable subgroup, a pair of conjugate subgroups, minimal inner-Σ-Ω-group MSC(2000): 20D10, 20D15Citation: Li X H, Xu Y. Minimal inner-Σ-Ω-groups and their applications.