ABOUT CHARACTERS ON VILENKIN GROUPS - Pepić, Medo (Matematichki Bilten, 2008)
In this paper we proved that Lemma [7, p.727] is not true and that the following Theorem holds: Let \(G\) be Vilenkin group. Let \(k [m_n,m_n+1)\) be natural number given by \[ k=_j=0^nk_jm_j,1≤ k_n<p_n+1;0≤ k_j<p_j+1, \] \(j{0,1,2,…,n-1}\) and let \(k\) be natural number such that \((xG)\) \[ χ_k(x)·χ_k (x)=1. \] In this case \(k=m_n+1-k+m_n-1\). Additionally, we have proved lemma which can be useful independently from our theorem.