The Frattini subgroups of linear Noetherian groups
نویسندگان
چکیده
منابع مشابه
Abelian groups have/are near Frattini subgroups
The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.
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Let Γg,b denote the orientation-preserving Mapping Class Group of a closed orientable surface of genus g with b punctures. For a group G let Φf (G) denote the intersection of all maximal subgroups of finite index in G. Motivated by a question of Ivanov as to whether Φf (G) is nilpotent when G is a finitely generated subgroup of Γg,b, in this paper we compute Φf (G) for certain subgroups of Γg,b...
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Let G = A ∗H B be the generalized free product of the groups A and B with the amalgamated subgroup H. Also, let λ(G) and ψ(G) represent the lower near Frattini subgroup of G and the near Frattini subgroup of G respectively. We show that G is ψ−free provided: (i) G is any ordinary free product of groups; (ii) G = A ∗H B and there exists an element c in G\H such thatH ∩H = 1; (iii) G = A ∗H B and...
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A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.
متن کاملConjectures and Questions Regarding Near Frattini Subgroups of Generalized Free Products of Groups
Let G = A ∗H B be the generalized free product of the groups A and B with the amalgamated subgroup H. Also, let λ(G), μ(G), ψ(G), K(G,H), and Tor H represent the lower near Frattini subgroup of G, the upper near Frattini subgroup of G, the near Frattini subgroup of G, the core of H in G, and the torsion subgroup of H, respectively. Since 1990 a series of papers have been published by the author...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1971
ISSN: 0022-314X
DOI: 10.1016/0022-314x(71)90052-7