On the Construction of Cyclic Algebras with a Given Exponent

1932 ◽  
Vol 54 (1) ◽  
pp. 1 ◽  
Author(s):  
A. Adrian Albert
Keyword(s):  
Cyclic Algebras

scholarly journals Galois realizability of groups of orders p 5 and p 6

2013 ◽  
Vol 11 (5) ◽  
Author(s):  
Ivo Michailov
Keyword(s):  
Galois Groups ◽  
Roots Of Unity ◽  
Arbitrary Field ◽  
Cyclic Algebras

AbstractLet p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.

On theu-invariant for quadratic forms and the linkage of cyclic algebras

1993 ◽  
Vol 214 (1) ◽  
pp. 137-146
Author(s):  
Roberto Aravire ◽  
Bill Jacob ◽  
Pasquale Mammone
Keyword(s):  
Quadratic Forms ◽  
Cyclic Algebras
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