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...
متن کاملNear Frattini Subgroups of Certain 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) 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...
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...
متن کاملNear Frattini Subgroups of Residually Finite Generalized Free Products of Groups
Let G = A HB 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 and the near Frattini subgroup of G, respectively. If G is finitely generated and residually finite, then we show that ψ(G) ≤ H, provided H satisfies a nontrivial identical relation. Also, we prove that if G is residually finite, ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1993
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708950000999x