On the Influence of Transitively Normal Subgroups on the Structure of Some Infinite Groups
نویسندگان
چکیده
A transitively normal subgroup of a group G is one that is normal in every subgroup in which it is subnormal. This concept is obviously related to the transitivity of normality because the latter holds in every subgroup of a group G if and only if every subgroup of G is transitively normal. In this paper we describe the structure of a group whose cyclic subgroups (or a part of them) are transitively normal. 2010 Mathematics Subject Classification: Primary: 20E15; Secondary: 20F16, 20F19.
منابع مشابه
The influence of S-embedded subgroups on the structure of finite groups
Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...
متن کاملON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...
متن کاملOn the type of conjugacy classes and the set of indices of maximal subgroups
Let $G$ be a finite group. By $MT(G)=(m_1,cdots,m_k)$ we denote the type of conjugacy classes of maximal subgroups of $G$, which implies that $G$ has exactly $k$ conjugacy classes of maximal subgroups and $m_1,ldots,m_k$ are the numbers of conjugates of maximal subgroups of $G$, where $m_1leqcdotsleq m_k$. In this paper, we give some new characterizations of finite groups by ...
متن کاملOn the eigenvalues of normal edge-transitive Cayley graphs
A graph $Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-tra...
متن کاملFinite groups with $X$-quasipermutable subgroups of prime power order
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...
متن کامل