scholarly journals On the non–periodic groups, whose subgroups of infinite special rank are transitively normal

2020 ◽  
Vol 29 (1) ◽  
pp. 74-84
Author(s):  
L. A. Kurdachenko ◽  
◽  
I. Ya. Subbotin ◽  
T. V. Velychko ◽  
◽  
...  
Keyword(s):  
Special Rank ◽  
Periodic Groups

scholarly journals On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal

2021 ◽  
pp. 12-14
Author(s):  
T.V. Velychko
Keyword(s):  
Abelian Groups ◽  
Finitely Generated ◽  
Special Rank ◽  
Periodic Groups

A group G has a finite special rank r, if every finitely generated subgroup of G can be generated by at most r elements, and there exists a finitely generated subgroup H which has exactly r generators. This paper is devoted to genera lized radical non-Abelian groups of infinite special rank whose subgroups of infinite special rank are transitively normal.

scholarly journals On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal

2021 ◽  
Vol 13 (2) ◽  
pp. 515-521
Author(s):  
T.V. Velychko
Keyword(s):  
Abelian Groups ◽  
Finitely Generated ◽  
Special Rank ◽  
Periodic Groups

A group $G$ has a finite special rank $r$ if every finitely generated subgroup of $G$ is generated by at most $r$ elements and there is a finitely generated subgroup of $G$ which has exactly $r$ generators. If there is not such $r$, then we say that $G$ has infinite special rank. In this paper, we study generalized radical non-abelian groups of infinite special rank whose subgroups of infinite special rank are transitively normal.

scholarly journals Certain locally nilpotent varieties of groups

2003 ◽  
Vol 67 (1) ◽  
pp. 115-119
Author(s):  
Alireza Abdollahi
Keyword(s):  
Prime Power ◽  
Power Exponent ◽  
Variety Of Groups ◽  
Periodic Groups ◽  
Locally Nilpotent

Let c ≥ 0, d ≥ 2 be integers and be the variety of groups in which every d-generator subgroup is nilpotent of class at most c. N.D. Gupta asked for what values of c and d is it true that is locally nilpotent? We prove that if c ≤ 2d + 2d−1 − 3 then the variety is locally nilpotent and we reduce the question of Gupta about the periodic groups in to the prime power exponent groups in this variety.

Finite automata and Burnside's problem for periodic groups

1972 ◽  
Vol 11 (3) ◽  
pp. 199-203 ◽  
Author(s):  
S. V. Aleshin
Keyword(s):  
Finite Automata ◽  
Periodic Groups

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.

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