On the connection between periodic groups and Lie rings

1965 ◽  
pp. 165-189 ◽  
Author(s):  
A. I. Kostrikin
Keyword(s):  
Lie Rings ◽  
Periodic Groups

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

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

Varieties of solvable Lie rings of finite width

1998 ◽  
Vol 63 (5) ◽  
pp. 569-574
Author(s):  
D. S. Ananichev ◽  
M. V. Volkov
Keyword(s):  
Finite Width ◽  
Lie Rings

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 Color Lie rings and PBW deformations of skew group algebras

2019 ◽  
Vol 518 ◽  
pp. 211-236
Author(s):  
S. Fryer ◽  
T. Kanstrup ◽  
E. Kirkman ◽  
A.V. Shepler ◽  
S. Witherspoon
Keyword(s):  
Group Algebras ◽  
Lie Rings ◽  
Skew Group Algebras
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