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کاربرد نوع شرط:
- 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,Soluble group,Sylow subgroup
- چکیده:
- چکیده انگلیسی: In this paper, groups with trivial intersection between Frattini and derived subgroups are considered. First, some structural properties of these groups are given in an important special case. Then, some family invariants of each $n$-isoclinism family of such groups are stated. In particular, an explicit bound for the order of each center factor group in terms of the order of its derived subgroup is also provided.
- انتشار مقاله: 09-08-1397
- نویسندگان: Azam Kaheni,Farangis Johari
- مشاهده