منابع مشابه
Frattini-based starters in 2-groups
Let G be a finite group of even order v. Does there exist a 1−factorization of Kv admitting G as an automorphism group acting sharply transitively on vertices? If G is cyclic and v = 2, for t ≥ 3, then the answer to the previous question is known to be negative by a result of A.Hartman and A.Rosa (1985). For several large families of groups of even order constructions have always been found thu...
متن کاملOn central Frattini extensions of finite groups
An extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H . The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G...
متن کاملAbelian 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.
متن کاملFrattini and related subgroups of Mapping Class Groups
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 کاملRecognizing PSL(2, p) in the non-Frattini chief factors of finite groups
Given a finite group G, let PG(s) be the probability that s randomly chosen elements generate G, and let H be a finite group with PG(s) = PH(s). We show that if the nonabelian composition factors of G and H are PSL(2, p) for some non-Mersenne prime p ≥ 5, then G and H have the same non-Frattini chief factors. Mathematics Subject Classification (2010). 20D06.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.11.052