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 nth 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. Within a fixed algebraic closure,
these extensions correspond to finite subgroups
of 
, where 
is the multiplicative group of
nonzero elements of 
(Milne 2022, p. 75).
