Example of a null-series with respect to periodic multiplicative systems

1993 ◽  
Vol 54 (6) ◽  
pp. 1187-1191
Author(s):  
N. A. Bokaev ◽  
M. A. Nurkhanov
Keyword(s):  
Multiplicative Systems ◽  
Null Series

On multiplicative systems defined by generators and relations

1953 ◽  
Vol 49 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Trevor Evans
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Cyclic Group ◽  
Complete Information ◽  
Isomorphism Problem ◽  
Infinite Cyclic Group ◽  
Generators And Relations ◽  
Decision Method ◽  
Multiplicative Systems ◽  
Finitely Related

The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly complete information about the automorphisms and endo-morphisms of free and finitely related loops. The automorphism group of the free monogenie loop is the infinite cyclic group, each automorphism being obtained by mapping the generator on one of its repeated inverses. A monogenie loop with a finite, non-empty set of relations has only a finite number of endomorphisms. These are obtained by mapping the generator on some of the components, or their repeated inverses, occurring in the relations. We use the same methods to solve the isomorphism problem for monogenie loops, i.e. we give a method for determining whether two finitely related monogenie loops are isomorphic. The decision method consists essentially of constructing all homomorphisms between two given finitely related monogenie loops.

Series in multiplicative systems in Lorentz spaces

2017 ◽  
Vol 102 (3-4) ◽  
pp. 310-324
Author(s):  
S. S. Volosivets
Keyword(s):  
Lorentz Spaces ◽  
Multiplicative Systems
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