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For an odd prime $p$ and polynomial $P(T)$, we consider the extension $F$ of$k={\mathbb F}_p(T)$ defined by adjoining a root of $x^p+Tx-P(T)$. Such a fieldis a function field analogue of the number field ${\mathbb Q}(\sqrt[p]{n})$. Weprove two theorems about the Galois closure $L$ of $F$: that its degree-0divisor class group is $A^{p-1}$ for some group $A$, and that its class numberis the $(p-1)$-st power of the class number of $F$, in analogy with results ofR. Schoof and T. Honda for number fields.

Class Group Relations in a Function Field Analogue of ${\mathbb Q}(\zeta_p, \sqrt[p]{n})$