On finite groups which contain a frobenius subgroup
نویسندگان
چکیده
منابع مشابه
Groups 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 $m^{th}$-autocommutator subgroup of finite abelian groups
Let $G$ be a group and $Aut(G)$ be the group of automorphisms of $G$. For any natural number $m$, the $m^{th}$-autocommutator subgroup of $G$ is defined as: $$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G,alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$ In this paper, we obtain the $m^{th}$-autocommutator subgroup of all finite abelian groups.
متن کاملRelative non-Normal Graphs of a Subgroup of Finite Groups
Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...
متن کاملOn Groups which contain no HNN-Extensions
A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. 23 We prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups. We also consider finitely generated groups with no free subsemigroups of rank 2 25 and show that in many situations such groups are virtually nilpotent. Finally, as an application of our results, we determine...
متن کاملON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1967
ISSN: 0021-8693
DOI: 10.1016/0021-8693(67)90004-x