A graph related to the join of subgroups of a finite group
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. ...
متن کاملon 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. ...
متن کاملOn 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 ∆(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 = ⟨H,K⟩. In this paper we classify finite groups with planar graph. Our result shows that only few groups have planar ...
متن کاملSOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP
Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...
متن کاملOn the norm of the derived subgroups of all subgroups of a finite group
In this paper, we give a complete proof of Theorem 4.1(ii) and a new elementary proof of Theorem 4.1(i) in [Li and Shen, On the intersection of the normalizers of the derived subgroups of all subgroups of a finite group, J. Algebra, 323 (2010) 1349--1357]. In addition, we also give a generalization of Baer's Theorem.
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ژورنال
عنوان ژورنال: Rendiconti del Seminario Matematico della Università di Padova
سال: 2014
ISSN: 0041-8994
DOI: 10.4171/rsmup/131-17