CAMINA p-groups that are generalized Frobenius complements

Let P be a Camina p-group that acts on a group Q in such a way that CP(x)⊆P′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{C}_P(x) \subseteq P'}$$\end{document} for all nonidentity elements x∈Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x \in Q}$$\end{document}. We show that P must be isomorphic to the quaternion group Q8. If P has class 2, this is a known result, and this paper corrects a previously published erroneous proof of the general case.