Let C be a conjugacy class of the symmetric group Sn . Recall that C consists of all of the permutations of a given cycle type.
Hence we may define the support of C, denoted by supp(C), to be the number of nonfixed digits under the action of a permutation in C.
If C has “large” support, then each element of C“moves” a lot of letters.
If the permutations in C are all even, then we say that C is an even conjugacy class. If the permutations in C are all odd, we say that C is an odd conjugacy class.
For n≥5, the subgroup generated by C, denoted by C, is Sn if C is odd, and An if C is even.
now we understand how turing thought about avalanche -and the significance of 4. he used gccs terms, like beetles….