On the join of subnormal subgroups
نویسندگان
چکیده
منابع مشابه
On the planarity of a graph related to the join of subgroups of a finite group
Let $G$ be a finite group which is not a cyclic $p$-group, $p$ a prime number. We define an undirected simple graph $Delta(G)$ whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=langle H , Krangle$. In this paper we classify finite groups with planar graph. ...
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Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0335650-9