Akbar Dehghan Nezhad - School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, ۱۶۸۴۶ -۱۳۱۱۴, Iran
Shiva Fatehi Boroujenib - Department of Mathematical Sciences, Yazd University, ۸۹۱۹۵--۷۴۱, Yazd, Iran
Alireza Ahmadi - Department of Mathematical Sciences, Yazd University, ۸۹۱۹۵--۷۴۱, Yazd, Iran

This work is intended to probe the connections between the diffeology and gyrogroup by introducing the notion of diffeological gyrogroup and proceeding with the study of some basic facts about it. The theory is developed by the study of smooth action of a diffeological gyrogroup.

diffeology, gyrogroups, diffeological gyrogroups, action of diffeological gyrogroups