A prime Baer group

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

scholarly journals Baer Group Rings with Involution

2017 ◽  
pp. 1-1
Author(s):  
Anil Khairnar ◽  
B. N. Waphare
Keyword(s):  
Group Rings ◽  
Baer Group ◽  
Rings With Involution

Groups with finitely many non-isomorphic factor-groups

2020 ◽  
pp. 2150223
Author(s):  
Leonid A. Kurdachenko ◽  
Patrizia Longobardi ◽  
Mercede Maj
Keyword(s):  
Finite Group ◽  
Metabelian Group ◽  
Chernikov Group ◽  
Baer Group

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.

scholarly journals Baer and quasi-Baer properties of group rings

2007 ◽  
Vol 83 (2) ◽  
pp. 285-296 ◽  
Author(s):  
Zhong Yi ◽  
Yiqiang Zhou
Keyword(s):  
Finite Group ◽  
Group Ring ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Group Rings ◽  
Baer Group ◽  
Baer Ring ◽  
Fixed Ring ◽  
A Finite Group ◽  
Left Annihilator

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.

Groups with small deviation for non-subnormal subgroups

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Howard Smith
Keyword(s):  
Small Deviation ◽  
Minimal Condition ◽  
Baer Group ◽  
Weak Minimal Condition ◽  
Locally Nilpotent ◽  
Torsion Free ◽  
Subnormal Subgroups

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.

scholarly journals Subnormality conditions in non-torsion groups

1999 ◽  
Vol 59 (3) ◽  
pp. 459-465 ◽  
Author(s):  
Luise-Charlotte Kappe ◽  
Gunnar Traustason
Keyword(s):  
Torsion Group ◽  
Nilpotency Class ◽  
Metabelian Groups ◽  
Baer Group ◽  
Engel Group ◽  
Torsion Groups

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.

ON GROUPS WHOSE PROPER SUBGROUPS ARE CHERNIKOV-BY-BAER OR (PERIODIC DIVISIBLE ABELIAN)-BY-BAER

2013 ◽  
Vol 12 (06) ◽  
pp. 1350015
Author(s):  
AHMET ARIKAN ◽  
NADIR TRABELSI
Keyword(s):  
Nilpotent Groups ◽  
Normal Closure ◽  
Maximal Subgroups ◽  
Locally Finite ◽  
Baer Group ◽  
Locally Nilpotent

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.

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