Frobenius introduced a canonical way of turning primes into conjugacy classes in Galois groups over Q. Specifically, if "K"/Q is a finite Galois extension then to each (positive) prime "p" which does not ramify in "K" and to each prime ideal "P" lying over "p" in "K" there is a unique element "g" of Gal("K"/Q) satisfying the condition "g"("x") = "x""p" (mod "P") for all integers "x" of "K". Varying "P" over "p" changes "g" into a conjugate (and every conjugate of "g" occurs in this way), so the conjugacy class of "g" in the Galois group is canonically associated to "p". This is called the Frobenius conjugacy class of "p" and any element of