On the number of solutions of equation in a finite group
Yakov Berkovich (1995)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
Theorem A yields the condition under which the number of solutions of equation in a finite -group is divisible by (here is a fixed positive integer). Theorem B which is due to Avinoam Mann generalizes the counting part of the Sylow Theorem. We show in Theorems C and D that congruences for the number of cyclic subgroups of order which are true for abelian groups hold for more general finite groups (for example for groups with abelian Sylow -subgroups).