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In this article, we announce our results on the Grothendieck-Teichmüller group GT obtained in the joint work with Yuichiro Hoshi and Shinichi Mochizuki. Let n ≥ 2 be a positive integer and k an algebraically closed field of characteristic zero. Write IIn for the étale fundamental group of the n-th configuration space of P1 k/{0, 1, 1∞} and Sn+3 for the symmetric group on n + 3 letters. Then our main theorem asserts that we have a direct product decomposition Out(IIn) = GT × Sn+3. The detail of the arguments appearing in this article may be found in [2]., Algebraic Number Theory and Related Topics 2017. December 4-8, 2017. edited by Hiroshi Tsunogai, Takao Yamazaki and Yasushi Mizusawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

In the present paper, the author introduces results concerning the indecomposability of various profinte groups related to hyperbolic curves. For instance, we discuss the indecomposability of the étale fundamental group of the configuration space of a hyperbolic curve over an algebraically closed field of characteristic zero, and the pro‐l Grothendieck - Teichmüller group. The details of the results and their proofs are given in [M]., 本稿では, 双曲的曲線に関連した様々な副有限群の非分解性についての結果を紹介する. 例えば, 標数 0 の代数閉体上の双曲的曲線に付随した配置空間のエタール基本群や副l グロタンディーク・タイヒミューラー群の非分解性について議論する. 結果や証明の詳細は[M]で与えられている., "Algebraic Number Theory and Related Topics 2015". November 30 - December 4, 2015. edited by Hiroki Takahashi, Yasuo Ohno and Takahiro Tsushima. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.