On Groups Saturated with Abelian Subgroups

1998 ◽  
Vol 08 (04) ◽  
pp. 443-466 ◽  
Author(s):  
Lev S. Kazarin ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Normal Subgroups ◽  
Main Subject ◽  
Maximal Condition ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Locally Nilpotent ◽  
Abelian Subgroups ◽  
Weak Maximal Condition

Groups with the weak maximal condition on non-abelian subgroups are the main subject of this research. Locally finite groups with this property are abelian or Chemikov. Non-abelian groups with the weak maximal condition on non-abelian subgroups, which have an ascending series of normal subgroups with locally nilpotent or locally finite factors, are described in this article.

scholarly journals On infinite groups in which all abelian subgroups are locally cyclic

2021 ◽  
Author(s):  
Costantino Delizia ◽  
Chiara Nicotera
Keyword(s):  
Finite Groups ◽  
Abelian Subgroup ◽  
Periodic Case ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Periodic Groups ◽  
Abelian Subgroups

AbstractThe structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

scholarly journals On locally finite groups factorized by locally nilpotent subgroups

1996 ◽  
Vol 106 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Silvana Franciosi ◽  
Francesco de Giovanni ◽  
Yaroslav P. Sysak
Keyword(s):  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Locally Nilpotent

Basis normalizers and Carter subgroups in a class of locally finite groups

1972 ◽  
Vol 71 (2) ◽  
pp. 189-198 ◽  
Author(s):  
C. J. Graddon ◽  
B. Hartley
Keyword(s):  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Finite Series ◽  
Locally Nilpotent ◽  
Image Position

We shall be working throughout this paper in the class of locally finite groups introduced in (3) and further discussed in (5) and (6), and all groups appearing will be assumed to belong to this class. By definition, is the largest subgroupclosed class of locally finite groups satisfying the conditions:U1. If G ε then G has a finite serieswith locally nilpotent factors.

scholarly journals Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups

2020 ◽  
Vol 23 (5) ◽  
pp. 831-846
Author(s):  
Anna Giordano Bruno ◽  
Flavio Salizzoni
Keyword(s):  
Finite Groups ◽  
Short Proof ◽  
Abelian Groups ◽  
Fundamental Property ◽  
The Other ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Algebraic Entropy ◽  
Finite Subgroups ◽  
Exact Sequences

AbstractAdditivity with respect to exact sequences is, notoriously, a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by using the structure theorems for such groups in an essential way. On the other hand, a solvable counterexample was recently found, showing that it does not hold in general. Nevertheless, we give a rather short proof of the additivity of algebraic entropy for locally finite groups that are either quasihamiltonian or FC-groups.

On the structure of groups whose non-abelian subgroups are subnormal

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Sevgi Atlıhan ◽  
Nikolaj Semko
Keyword(s):  
Finite Groups ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Abelian Subgroups

AbstractThe main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.

scholarly journals Uncountable existentially closed groups in locally finite group classes

1990 ◽  
Vol 32 (2) ◽  
pp. 153-163 ◽  
Author(s):  
Felix Leinen
Keyword(s):  
Finite Group ◽  
Wreath Product ◽  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Existentially Closed ◽  
Fixed Set ◽  
Locally Nilpotent ◽  
Closed Groups ◽  
Restrictive Type

In this paper, will always denote a local class of locally finite groups, which is closed with respect to subgroups, homomorphic images, extensions, and with respect to cartesian powers of finite -groups. Examples for x are the classes L ℐπ of all locally finite π-groups and L(ℐπ ∩ ) of all locally soluble π-groups (where π is a fixed set of primes). In [4], a wreath product construction was used in the study of existentially closed -groups (=e.c. -groups); the restrictive type of construction available in [4] permitted results for only countable groups. This drawback was then removed partially in [5] with the help of permutational products. Nevertheless, the techniques essentially only permitted amalgamation of -groups with locally nilpotent π-groups. Thus, satisfactory results could be obtained for Lp-groups (resp. locally nilpotent π-groups) [6], while the theory remained incomplete in all other cases.

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