منابع مشابه
A Generalized Frattini Subgroup of a Finite Group
For a finite group G and an arbitrary prime p, let S (G) denote the P intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set S (G) G. Some properties of P G are considered involving S (G). In particular, we obtain a characterization of P G when each M in the definition of S (G) is nilpotent. P
متن کاملThe Frattini Subgroup of a Group
In this paper, we review the behaviour of the Frattini subgroup Φ(G) and the Frattini factor group G/Φ(G) of an infinite group G having in mind the most standard results of the finite case. Este art́ıculo está dedicado con todo cariño a la memoria de Chicho. Al no formar parte de tu grupo de investigación, no tuve la fortuna de relacionarme contigo por este motivo, pero śı que tuve la oportunida...
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Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...
متن کاملGroups in which every subgroup has finite index in its Frattini closure
In 1970, Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 48 (1970), 559--562.] gave a complete description of the structure of soluble $IM$-groups, i.e., groups in which every subgroup can be obtained as intersection of maximal subgroups. A group $G$ is said to have the $FM$...
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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.09.010