CAJ | 학술논문

令ω是由有限个正整数组成的集合。如果1∈ω，且当s ∈ω时，s的每个正因子t ∈ω，则称ω是合理子集。用πe（K）表示由有限群K的元素的阶组成的集合。如果对于πe（G）的每个合理子集ω，都存在一个有限群 H ，使得πe（H）＝ω，则称有限群G是好群；如果对于πe（G）的每个合理子集ω，都存在G的子群H ，使得πe（H）＝ω，则称有限群 G是强好群。主要确定了某些好群和强好群。
령ω시유유한개정정수조성적집합。여과1∈ω，차당s ∈ω시，s적매개정인자t ∈ω，칙칭ω시합리자집。용πe（K）표시유유한군K적원소적계조성적집합。여과대우πe（G）적매개합리자집ω，도존재일개유한군 H ，사득πe（H）＝ω，칙칭유한군G시호군；여과대우πe（G）적매개합리자집ω，도존재G적자군H ，사득πe（H）＝ω，칙칭유한군 G시강호군。주요학정료모사호군화강호군。
Let ωbe a finite set of positive integers .ωis called a reasonable subset if it satisfies the following two conditions :1∈ ω,and when s∈ ω,t∈ ωfor each positive factor t of s .For a finite group K ,πe (K ) denotes the set of the orders of the elements in K .A finite group G is called a good group if for a reasona‐ble subset ωof πe (G) ,there is a finite group H such that πe (H )= ω.A finite group G is called a strong good group if for a reasonable subset ωof πe (G) there is a subgroup H of G such that πe (H )= ω.The main purpose of this paper is to determine some good groups and some strong good groups .