On the number of solutions of the equation $x^ {p^ k}=a$ in a finite $p$-group
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- by Yakov G. Berkovich PDF
- Proc. Amer. Math. Soc. 116 (1992), 585-590 Request permission
Abstract:
A. Kulakoff (Math. Ann. 104 (1931), 778-793) proved that for $p > 2$ the number of solutions of the equation ${x^{{p^k}}} = e$ ($e$ is a unit element of $G$) in a finite noncyclic $p$-group $G$ is divisible by ${p^{k + 1}}$ if $\operatorname {exp} G \geq {p^k}$. In this note we consider the number $N(a,G,k)$ of solutions of the equation ${x^{{p^k}}} = a$ in $G,\;a \in G$. Our results cover the case $p = 2$ also.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 585-590
- MSC: Primary 20D60; Secondary 20D15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1093592-9
- MathSciNet review: 1093592