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Joe Silverman
Joe Silverman
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Does the unit index divide the degree of an extension of number fields?

Let L/K$L/K$ be a finite extension of algebraic number fields of degree prime p$p$. Is it true that the index (U_K:Norm(U_L))$(U_K:\text{Norm}(U_L))$ divides [L:K]?$[L:K]$, where U_$U_K$ denotes the unit group and Norm denotes the ideal norm map of the relative extension of L/K.$L/K$?

Does unit index divide degree of extension?

Let L/K be a finite extension of algebraic number fields of degree prime p. Is it true the index (U_K:Norm(U_L)) divides [L:K]? where U_ denotes the unit group and Norm denotes the ideal norm map of relative extension of L/K.

Does the unit index divide the degree of an extension of number fields?

Let $L/K$ be a finite extension of algebraic number fields of degree prime $p$. Is it true that the index $(U_K:\text{Norm}(U_L))$ divides $[L:K]$, where $U_K$ denotes the unit group and Norm denotes the ideal norm map of the relative extension of $L/K$?

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A. Maarefparvar
A. Maarefparvar
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Does unit index divide degree of extension?

Let L/K be a finite extension of algebraic number fields of degree prime p. Is it true the index (U_K:Norm(U_L)) divides [L:K]? where U_ denotes the unit group and Norm denotes the ideal norm map of relative extension of L/K.