منابع مشابه
On 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.
متن کاملOn semi-$Pi$-property of subgroups of finite group
Let $G$ be a group and $H$ a subgroup of $G$. $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$. In this paper, investigating on semi-$Pi$-property of subgroups, we shall obtain some new description of finite groups.
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 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 کاملSubgroups of the Symmetric Group
We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1961
ISSN: 0002-9939
DOI: 10.2307/2034146