Periodic groups that satisfy the normalizer condition for pd-subgroups

1983 ◽  
Vol 34 (3) ◽  
pp. 648-650
Author(s):  
F. N. Liman
Keyword(s):  
Normalizer Condition ◽  
Periodic Groups

THE GROUPS WHOSE SUBGROUPS ARE ALMOST ASCENDANT

2013 ◽  
Vol 06 (01) ◽  
pp. 1350014 ◽  
Author(s):  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Finite Index ◽  
Periodic Group ◽  
Finite Subgroup ◽  
Normalizer Condition ◽  
Periodic Groups

A subgroup H of a group G is called almost ascendant if H is ascendant in a subgroup K having finite index in G. We describe the structure of periodic groups whose subgroups are almost ascendant. The main result of this paper is following theorem. Let G be a periodic group whose subgroups are almost ascendant. Then G contains a normal finite subgroup K such that every subgroup of G/K is ascendant in G/K. In particular, G/K satisfies the normalizer condition.

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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