Groups satisfying the minimal condition on subgroups which are not transitively normal
نویسندگان
چکیده
Abstract A subgroup X of a group G is called transitively normal if in any Y such that $$X\le Y$$ X≤Y and subnormal . Thus all subgroups are only normality transitive relation every (i.e. $$\overline{T}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">T¯ -group). It proved with no infinite simple sections satisfies the minimal condition on not either Černikov or $${\overline{T}}$$ -group.
منابع مشابه
On the Influence of Transitively Normal Subgroups on the Structure of Some Infinite Groups
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 transit...
متن کاملfinite groups whose minimal subgroups are weakly h*-subgroups
let $g$ be a finite group. a subgroup $h$ of $g$ is called an $mathcal h $ -subgroup in $g$ if $n_g (h)cap h^gleq h$ for all $gin g$. a subgroup $h$ of $g$ is called a weakly $mathcal h^ast $-subgroup in $g$ if there exists a subgroup $k$ of $g$ such that $g=hk$ and $hcap k$ is an $mathcal h$-subgroup in $g$. we investigate the structure of the finite group $g$ under the assump...
متن کاملOn Normal Subgroups Which Are Direct Products
Now that the classification of finite simple groups is complete, it is logical to look at the extension problem. An important special case to consider is when M is a minimal normal subgroup of G and both G/M and M are known groups. If M is abelian, various techniques have been used to derive information about G. Indeed, almost the entire theory of finite solvable groups can be said to rest upon...
متن کاملFINITE p-GROUPS WHICH ARE NOT GENERATED BY THEIR NON-NORMAL SUBGROUPS
Here we classify finite non-Dedekindian p-groups which are not generated by their non-normal subgroups. (Theorem 1). The purpose of this paper is to classify non-Dedekindian finite p-groups which are not generated by their non-normal subgroups. It is surprising that such p-groups must be of class 2 with a cyclic commutator subgroup. We consider here only finite p-groups and our notation is stan...
متن کاملNormal Subgroups of the Modular Group Which Are Not Congruence Subgroups
A subgroup of V containing a principal congruence subgroup T(«) is said to be a congruence subgroup, and is of level « if « is the least such integer. In a recent article [2] the writer determined all normal subgroups of T of genus 1 (see [l] for the definition of the genus of a subgroup of r). An interesting question that arises is to decide which of these are also congruence subgroups. In thi...
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: Rendiconti Del Circolo Matematico Di Palermo
سال: 2021
ISSN: ['1973-4409', '0009-725X']
DOI: https://doi.org/10.1007/s12215-021-00602-0