scholarly journals Normal Ω-subgroups

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6699-6711
Author(s):  
Omalkhear Bleblou ◽  
Branimir Seselja ◽  
Andreja Tepavcevic
Keyword(s):  
Normal Subgroup ◽  
Minimal Normal Subgroup ◽  
Normal Subgroups ◽  
Algebraic Structures ◽  
Quotient Groups

Subgroups, congruences and normal subgroups are investigated for-groups. These are latticevalued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal ?-subgroup is defined as a particular class in an ?-congruence. Our main result is that the quotient groups over cuts of a normal ?-subgroup of an ?-group G?, are classical normal subgroups of the corresponding quotient groups over G?. We also describe the minimal normal ?-subgroup of an ?-group, and some other constructions related to ?-valued congruences.

scholarly journals On Prefrattini residuals

1998 ◽  
Vol 40 (2) ◽  
pp. 187-197
Author(s):  
A. Ballester-Bolinches ◽  
H. Bechtell ◽  
L. M. Ezquerro
Keyword(s):  
Normal Subgroup ◽  
Maximal Subgroup ◽  
Finite Groups ◽  
Minimal Normal Subgroup ◽  
Classification Problem ◽  
Chief Factor ◽  
Maximal Subgroups ◽  
Normal Subgroups ◽  
Chief Factors ◽  
Will Force

All groups considered in the sequel are finite. Let (ℭ and denote the formations of groups which consist of collections of groups that respectively either split over each normal subgroup (nC-groups) or for which the groups do not possess nontrivial Frattini chief factors [8]. The purpose of this article is to develop and expand a concept that arises naturally with the residuals for these formations, namely each G-chief factor is non-complemented (Frattini). With respect to a solid set X of maximal subgroups, these properties are generalized respectively to so-called X-parafrattini (X-profrattini) normal subgroups for which each type is closed relative to products. The relationships among the unique maximal normal subgroups that result from these products, the solid set of maximal subgroups X, X-prefrattini subgroups, and the residuals of formations are explored. This leads to a well-defined collected of formations, the partially nonsaturated formations, with properties analogous to those which are totally non-saturated. In the development, attention is given to a set of maximal subgroups which is the image of a solid function defined on all groups, a weaker condition than that of a solid set. A result of particular interest answers affirmatively the long-standing conjecture that a non-trivial nC-group G is solvable if and only if each G-chief factor is complemented by a maximal subgroup. This will force a critical re-examination of the classification problem for nC-groups. Since the article continues the investigations on finite groups initiated in [2], a familiarity with that article is assumed. All other notation and terminology is from [6]. If M is a maximal subgroup of a group G and G/C or e G(M) is a monolithic primitive group, i.e. a group with a unique minimal normal subgroup, then M is called a monolithic maximal subgroupof G.

COMPONENTS AND MINIMAL NORMAL SUBGROUPS OF FINITE AND PSEUDOFINITE GROUPS

2019 ◽  
Vol 84 (1) ◽  
pp. 290-300
Author(s):  
JOHN S. WILSON
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Minimal Normal Subgroup ◽  
Normal Subgroups ◽  
First Order ◽  
Order Language ◽  
Image Position ◽  
A Finite Group

AbstractIt is proved that there is a formula$\pi \left( {h,x} \right)$in the first-order language of group theory such that each component and each non-abelian minimal normal subgroup of a finite groupGis definable by$\pi \left( {h,x} \right)$for a suitable elementhofG; in other words, each such subgroup has the form$\left\{ {x|x\pi \left( {h,x} \right)} \right\}$for someh. A number of consequences for infinite models of the theory of finite groups are described.

A note on automorphism groups of symmetric cubic graphs

2020 ◽  
pp. 2250018
Author(s):  
Jicheng Ma
Keyword(s):  
Automorphism Group ◽  
Normal Subgroup ◽  
Simple Group ◽  
Minimal Normal Subgroup ◽  
Automorphism Groups ◽  
Cubic Graphs ◽  
Normal Subgroups ◽  
Interesting Consequence ◽  
Cubic Graph

We study [Formula: see text]-arc-transitive cubic graph [Formula: see text], and give a characterization of minimal normal subgroups of the automorphism group. In particular, each [Formula: see text] with quasi-primitive automorphism group is characterized. An interesting consequence of this characterization states that a non-solvable minimal normal subgroup [Formula: see text] contains at most 2 copies of non-abelian simple group when it acts transitively on arcs, or contains at most 6 copies of non-abelian simple group when it acts regularly on vertices.

scholarly journals GRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY

2019 ◽  
Vol 13 (1) ◽  
pp. 1
Author(s):  
Mahfuz Tarmizi ◽  
Saman Abdurrahman
Keyword(s):  
Normal Subgroup ◽  
Quotient Group ◽  
Binary Operation ◽  
Normal Subgroups ◽  
Quotient Groups

A Quotient group is a set which contains coset members and satisfies group definition. These cosets are formed by group and its normal subgroup. A set which contains fuzzy coset members is also called a quotient group. These fuzzy cosets are formed by a group and its fuzzy normal subgroup. The purpose of this research is to explain quotient groups induced by fuzzy normal subgroups and isomorphic between them. This research construct sets which contain fuzzy coset members, define an operation between fuzzy cosets and prove these sets under an operation between fuzzy coset satisfy group definition, and prove theorems relating to qoutient groups and homomorphism. The results of this research are  is a qoutient group induced by a fuzzy normal subgroup, where  is a fuzzy normal subgroup of a group ,  is a fuzzy coset, and the binary operation is “” where  for every . An epimorphism  from a group  to a group  and a fuzzy normal subgroup  of  which is constant on  cause quotient goup  and   are isomorphic.

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

Quotient groups and realization of tight Riesz groups

1973 ◽  
Vol 16 (4) ◽  
pp. 416-430 ◽  
Author(s):  
John Boris Miller
Keyword(s):  
Normal Subgroup ◽  
Open Interval ◽  
Canonical Homomorphism ◽  
Interval Topology ◽  
Essential Step ◽  
Image Position ◽  
Quotient Groups

Let (G, ≼) be an l-group having a compatible tight Riesz order ≦ with open-interval topology U, and H a normal subgroup. The first part of the paper concerns the question: Under what conditions on H is the structure of (G, ≼, ∧, ∨, ≦, U) carried over satisfactorily to by the canonical homomorphism; and its answer (Theorem 8°): H should be an l-ideal of (G, ≼) closed and not open in (G, U). Such a normal subgroup is here called a tangent. An essential step is to show that ≼′ is the associated order of ≦′.

scholarly journals On groups, whose non-normal subgroups are either contranormal or core-free

2020 ◽  
pp. 3-8
Author(s):  
L.A. Kurdachenko ◽  
◽  
A.A. Pypka ◽  
I.Ya. Subbotin ◽  
◽  
...  
Keyword(s):  
Normal Subgroup ◽  
Normal Subgroups

We investigate the influence of some natural types of subgroups on the structure of groups. A subgroup H of a group G is called contranormal in G, if G = HG. A subgroup H of a group G is called core-free in G, if CoreG(H) =〈1〉. We study the groups, in which every non-normal subgroup is either contranormal or core-free. In particular, we obtain the structure of some monolithic and non-monolithic groups with this property

On normal subgroups of M-groups

2019 ◽  
Vol 18 (04) ◽  
pp. 1950074
Author(s):  
Xuewu Chang
Keyword(s):  
Normal Subgroup ◽  
Solvable Group ◽  
Solvable Groups ◽  
Hall Subgroup ◽  
Embedding Theorem ◽  
The Other ◽  
Finite Solvable Group ◽  
Embedding Problem ◽  
Normal Subgroups ◽  
Other Hand

The normal embedding problem of finite solvable groups into [Formula: see text]-groups was studied. It was proved that for a finite solvable group [Formula: see text], if [Formula: see text] has a special normal nilpotent Hall subgroup, then [Formula: see text] cannot be a normal subgroup of any [Formula: see text]-group; on the other hand, if [Formula: see text] has a maximal normal subgroup which is an [Formula: see text]-group, then [Formula: see text] can occur as a normal subgroup of an [Formula: see text]-group under some suitable conditions. The results generalize the normal embedding theorem on solvable minimal non-[Formula: see text]-groups to arbitrary [Formula: see text]-groups due to van der Waall, and also cover the famous counterexample given by Dade and van der Waall independently to the Dornhoff’s conjecture which states that normal subgroups of arbitrary [Formula: see text]-groups must be [Formula: see text]-groups.

Elementary amenable groups and 4-manifolds with Euler characteristic 0

1991 ◽  
Vol 50 (1) ◽  
pp. 160-170 ◽  
Author(s):  
Jonathan A. Hillman
Keyword(s):  
Normal Subgroup ◽  
Fundamental Group ◽  
Euler Characteristic ◽  
Fundamental Groups ◽  
Normal Subgroups ◽  
Euler Characteristics ◽  
Amenable Groups ◽  
Amenable Subgroup ◽  
Finite Subgroups ◽  
Torsion Free

AbstractWe extend earlier work relating asphericity and Euler characteristics for finite complexes whose fundamental groups have nontrivial torsion free abelian normal subgroups. In particular a finitely presentable group which has a nontrivial elementary amenable subgroup whose finite subgroups have bounded order and with no nontrivial finite normal subgroup must have deficiency at most 1, and if it has a presentation of deficiency 1 then the corresponding 2-complex is aspherical. Similarly if the fundamental group of a closed 4-manifold with Euler characteristic 0 is virtually torsion free and elementary amenable then it either has 2 ends or is virtually an extension of Z by a subgroup of Q, or the manifold is asphencal and the group is virtually poly- Z of Hirsch length 4.

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