Abstract: This work summarizes some statements with respect to Fourier analysis on the complete product of not necessarily commutative finite groups, achieved recently. In particular we devotes attention to a concrete case: the complete product of the symmetric group on 3 elements. The aim of this work is to emphasize the differences between this noncommutative structure and the commutative cases.
Keywords: Fourier analysis, symmetric group, noncommutative structure, Walsh-Paley system.