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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Frattini subgroup,Baer's theorem,Upper and lower central series
- چکیده:
- چکیده انگلیسی: In 2012, Guo and Gong proved that if $G$ is a finite nonabelian group with $Phi(G)=1$, then $|G:Z(G)|<|G'||U(G)|$, in which $U(G)$ is the nilpotent residual of $G$. We show that the assumption of finiteness of the group can be omitted. Moreover, we investigate converse of Schur and Baer's theorems for groups that can be seen as generalizations of groups with trivial Frattini subgroups and state some properties of $n$-isoclinism families of these groups.
- انتشار مقاله: 09-01-1398
- نویسندگان: Yasaman Taghavi,Saeed Kayvanfar,Marzieh Chakaneh
- مشاهده