@article{article_455956, title={Central Automorphism Groups for Semidirect Product of p-Groups}, journal={The Eurasia Proceedings of Science Technology Engineering and Mathematics}, pages={288–289}, year={2018}, author={Oztekın, Ozge and Gurbuz, Zeynep}, keywords={P-group,Semi-direct product}, abstract={<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;text-align: justify;line-height:normal">Let <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>p² </sub> <span style="font-family: "Cambria Math", serif;">⋊ </span> <sub>ϕ </sub> <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>p </sub> be the semi-direct product of <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>p² </sub> and <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>p </sub> with respect to ϕ, (ϕ is homomorphism from <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>p </sub> to automorphisms group of <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>p² </sub>). In this work, the group Aut <sub>C </sub>( <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>3² </sub> <span style="font-family: "Cambria Math", serif;">⋊ </span> <sub>ϕ </sub> <span style="font-family: "Cambria Math", serif;">ℤ₃ </span>) of all central automorphisms of <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>3² </sub> <span style="font-family: "Cambria Math", serif;">⋊ </span> <sub>ϕ </sub> <span style="font-family: "Cambria Math", serif;">ℤ₃ </span> is studied and we determine the form of central automorphisms of <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>3² </sub> <span style="font-family: "Cambria Math", serif;">⋊ </span> <sub>ϕ </sub> <span style="font-family: "Cambria Math", serif;">ℤ </span> <sub>3 </sub> .  <o:p> </o:p> </p>}, number={2}, publisher={ISRES Publishing}