On the number of solutions of the equation 𝑥^{𝑝^{𝑘}}=𝑎 in a finite 𝑝-group
| Autor: | Yakov G. Berkovich |
|---|---|
| Rok vydání: | 1992 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 116:585-590 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1992-1093592-9 |
| Popis: | A. Kulakoff (Math. Ann. 104 (1931), 778-793) proved that for p > 2 p > 2 the number of solutions of the equation x p k = e {x^{{p^k}}} = e ( e e is a unit element of G G ) in a finite noncyclic p p -group G G is divisible by p k + 1 {p^{k + 1}} if exp G ≥ p k \operatorname {exp} G \geq {p^k} . In this note we consider the number N ( a , G , k ) N(a,G,k) of solutions of the equation x p k = a {x^{{p^k}}} = a in G , a ∈ G G,\;a \in G . Our results cover the case p = 2 p = 2 also. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|