This note presents the study of the conjugacy classes of elements of some given finite order n in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if n is even, n = 3 or n = 5, and that it is equal to 3 (respectively 9) if n = 9 (respectively 15), and is exactly 1 for all remaining odd orders. Some precise representative elements of the...

A conjugacy class C of a finite group G is a sign conjugacy class if every irreducible character of G takes value 0, 1 or −1 on C. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson.