Divisibility results on the number of conjugacy classes in finite groups
Let \(G\) be a finite group and let \(p_1,\dots,p_m\) be the primes dividing some integer \(n\). We show that the number of conjugacy classes of elements of order \(n\) is a multiple of \(\prod^m_{i=1}{p_i-1\over\text{gcd}(|G|,p_i-1)}\). We also relate the number of conjugacy classes \(k_G\) of \(G\) to \(k_N\), where \(N\) is a normal subgroup. These results yield corollaries related to the work of Mann and Vera Lopez.
scientific article; zbMATH DE number 938570