We report on a common fragment ion formed during the electron-ionization-induced fragmentation of three different three-ring polycyclic aromatic hydrocarbons (PAHs), fluorene (C$_{13}$H$_{10}$), 9,10-dihydrophenanthrene (C$_{14}$H$_{12}$), and 9,10-dihydroanthracene (C$_{14}$H$_{12}$). The infrared spectra of the mass-isolated product ions with $m/z=165$ were obtained in a Fourier transform ion cyclotron resonance mass spectrometer whose cell was placed inside the optical cavity of an infrared free-electron laser, thus providing the high photon fluence required for efficient infrared multiple-photon dissociation. The infrared spectra of the $m/z=165$ species generated from the three different precursors were found to be similar, suggesting the formation of a single C$_{13}$H$_{9}^+$ isomer. Theoretical calculations using density functional theory (DFT) revealed the fragments identity as the closed-shell fluorenyl cation. Decomposition pathways from each parent precursor to the fluorenyl ion are proposed on the basis of DFT calculations. The identification of a single fragmentation product from three different PAHs supports the notion of the existence of common decomposition pathways of PAHs in general and can aid in understanding the fragmentation chemistry of astronomical PAH species.
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