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Yayın Matching of Cocycle Extensions for Second Tangent Groups(American Institute of Physics Inc., 2022) Uçgun, F.Ç.; Esen, O.; Sütlü, S.We present the second-order tangent group of a Lie group as a cocycle extension of the first-order tangent group. We exhibit matching of the second-order tangent groups of two mutually interacting Lie groups. We examine the cocycle extension character of the matched second-order group and arrive at that matched pair of cocycle extensions is a cocycle extension by itself. © 2022 American Institute of Physics Inc.. All rights reserved.