On the History of the Discovery of the Subgroups of the Euclidean Group

  • José M. RicoEmail author
  • J. Jesús Cervantes-Sánchez
  • Emilia Olivares-Conraud
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


In the kinematics literature and community it is commonly accepted that the first complete list of the subgroups of the Euclidean group is due to Hervé, who in 1978, published a seminal paper on the applications of group theory to the mobility of kinematic chains. This contribution shows that, in the mathematical and physics communities, the determination of the subgroups of the Euclidean group is dated a century before, 1868, and it is the result of another French engineer and mathematician Camille Jordan. The only remaining issues, with Jordan’s contribution are that He also included a, latter proven, incomplete list of the finite subgroups of the Euclidean group and that the group concept as a mathematical structure was not completely agreed until 1900.


group theory subgroups kinematics mathematical history 


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The authors thank the Universidad de Guanajuato for its support. In addition, the first two authors thank, SNI, the Mexican National Systems of Researchers and CONACYT, National Council of Science and Technology for their support through fellowships and scholarships in the last few years.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • José M. Rico
    • 1
    Email author
  • J. Jesús Cervantes-Sánchez
    • 1
  • Emilia Olivares-Conraud
    • 1
  1. 1.Departamento de Ingeniería Mecánica, División de Ingenierías, CISUniversidad de GuanajuatoSalamancaMexico

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