A Kummer extension of a field 
containing the 
th roots of unity, where 
is a positive
integer not divisible by the characteristic
of 
,
is a field extension obtained by adjoining one
or more 
th
roots of elements of 
. In the simple case it has the form
 |
Finite Abelian extensions whose Galois groups have exponent dividing 
arise in this way, and their subgroups
can be described using classes in 
.
