Groups where each element is conjugate to its certain power. (Q386375)

This paper concerns the finite solvable groups \(G\) with the property that for a fixed positive integer \(n\) every element \(g\) of \(G\) is conjugate to its \(n\)-th power \(g^n\). The main result of the paper is that if \(p\) is any prime divisor of the order of \(G\), then either \(p\) divides \(n^{2(n-1)}-1\) or \(n^{3(n-1)}-1\).