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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Mathematics Interdisciplinary Research
- نوع مقاله: Journal Article
- کلمات کلیدی: Frattini subgroup,Sylow subgroup,n-Capable group
- چکیده:
- چکیده انگلیسی: Following P. Hall a soluble group whose Sylow subgroups are all abelian is called A-group. The purpose of this article is to give a new and shorter proof for a criterion on the capability of A-groups of order p^2q, where p and q are distinct primes. Subsequently we give a sufficient condition for n-capability of groups having the property that their center and derived subgroups have trivial intersection, like the groups with trivial Frattini subgroup and A-groups. An interesting necessary and sufficient condition for capability of the A-groups of square free order will be also given.
- انتشار مقاله: 01-08-1399
- نویسندگان: Marzieh Chakaneh,Saeed Kayvanfar,Rasoul Hatamian
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Capable group,n-isoclinism,Extra special p-group,Schur's theorem
- چکیده:
- چکیده انگلیسی: A famous theorem of Schur states that for a group $G$ finiteness of $G/Z(G)$ implies the finiteness of $G'.$ The converse of Schur's theorem is an interesting problem which has been considered by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur's theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur's theorem and at the same time admit the Podoski and Szegedy's bound as the upper bound for the index of their centers.
- انتشار مقاله: 23-02-1391
- نویسندگان: Azam Kaheni,Rasoul Hatamian,Saeed Kayvanfar
- مشاهده
- 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