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I read the book 'The Genesis of the Abstract Group Concept'. If you see page 91 of this book,

I wish to comment on the last two sections of Cauchy's paper. Both sections deal with a kind of anticipation of representation theory, namely, with what Serret and Jordan would later call "analytic representation of substitutions" and with what would occupy much space in Jordan's Traite des substitutions of 1870.

You can see the above paragraph. In this paragraph, I thought that Cauchy was the first person to develop the theory on which representation theory is based. So, I want to know whether Cauchy was the first person to create the theory that is the basis of representation theory and its overall flow. Of course, I know from here that Frobenius created modern representation theory. But I want to know even more about the history of the past.

Additionally, I found a site detailing Cauchy's accomplishments. The title is "The mathematical life of Cauchy's group theorem".

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    $\begingroup$ You can find 'anticipations' in Lagrange and Gauss even before Cauchy, see chapter 1 of Curtis, Pioneers of Representation Theory. But the idea of searching for "the first" is misguided:"The hope of finding a 'first' comes to grief because of the historically dynamic character of ideas... If we describe a result with sufficient vagueness, there seems to be an endless sequence of those who had something within the vague specifications", May, Historiographic Vices: Priority Chasing. $\endgroup$
    – Conifold
    Commented May 27 at 5:45
  • $\begingroup$ @Conifold Thank you very much for writing a comment. I will keep in mind what you said. $\endgroup$ Commented May 27 at 6:00

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