baer group
Recently Published Documents


TOTAL DOCUMENTS

7
(FIVE YEARS 0)

H-INDEX

2
(FIVE YEARS 0)

Author(s):  
Leonid A. Kurdachenko ◽  
Patrizia Longobardi ◽  
Mercede Maj

We prove that if [Formula: see text] is either a hypercentral-by-finite group or a soluble Baer group and if [Formula: see text] has finitely many non-isomorphic factor-groups, then [Formula: see text] is a Chernikov group. The converse is also true. Furthermore, we give some information on the structure of a metabelian group with finitely many non-isomorphic factor-groups.



Author(s):  
Anil Khairnar ◽  
B. N. Waphare


2013 ◽  
Vol 12 (06) ◽  
pp. 1350015
Author(s):  
AHMET ARIKAN ◽  
NADIR TRABELSI

If 𝔛 is a class of groups, then a group G is called a minimal non-𝔛-group if it is not an 𝔛-group but all of its proper subgroups belong to 𝔛. In this paper we prove that locally graded minimal non-(Chernikov-by-nilpotent)-groups are precisely minimal non-nilpotent-groups without maximal subgroups and that locally graded minimal non-(Chernikov-by-Baer)-groups are locally finite and coincide with the normal closure of an element. We also prove that an infinite locally graded minimal non-((periodic divisible abelian)-by-Baer)-group G is an imperfect locally nilpotent p-group, for some prime p, and there is an element a in G such that G = 〈a〉G.



2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Howard Smith

AbstractWe introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.



2007 ◽  
Vol 83 (2) ◽  
pp. 285-296 ◽  
Author(s):  
Zhong Yi ◽  
Yiqiang Zhou

AbstractA ring R is said to be a Baer (respectively, quasi-Baer) ring if the left annihilator of any nonempty subset (respectively, any ideal) of R is generated by an idempotent. It is first proved that for a ring R and a group G, if a group ring RG is (quasi-) Baer then so is R; if in addition G is finite then |G|–1 € R. Counter examples are then given to answer Hirano's question which asks whether the group ring RG is (quasi-) Baer if R is (quasi-) Baer and G is a finite group with |G|–1 € R. Further, efforts have been made towards answering the question of when the group ring RG of a finite group G is (quasi-) Baer, and various (quasi-) Baer group rings are identified. For the case where G is a group acting on R as automorphisms, some sufficient conditions are given for the fixed ring RG to be Baer.



1999 ◽  
Vol 59 (3) ◽  
pp. 459-465 ◽  
Author(s):  
Luise-Charlotte Kappe ◽  
Gunnar Traustason

According to results of Heineken and Stadelmann, a non-torsion group is a 2-Baer group if and only if it is 2-Engel, and it has all subgroups 2-subnormal if and only if it is nilpotent of class 2. We extend some of these results to values of n greater than 2. Any non-torsion group which is an n-Baer group is an n-Engel group. The converse holds for n = 3, and for all n in the case of metabelian groups. A non-torsion group without involutions having all subgroups 3-subnormal has nilpotency class 4, and this bound is sharp.



1968 ◽  
Vol 105 (4) ◽  
pp. 294-298 ◽  
Author(s):  
R. S. Dark
Keyword(s):  


Sign in / Sign up

Export Citation Format

Share Document