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What is the history of the homomorphism concept and who coined the term? I seem to be thinking it arose in abstract algebra and groups/rings/fields, but at what time and by whom? People like Galois and Cauchy pioneered these fields but I understand the concept of function itself wasn't even that precise until Dedekind who was much later than them.

Masacroso
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Ginkgo Biloba
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  • Try https://math.stackexchange.com/a/388462/589 – lhf Apr 23 '18 at 23:44
  • See https://mathoverflow.net/questions/280261/whence-homomorphism-and-homomorphic and https://mathoverflow.net/questions/290471/who-first-used-the-word-homomorphism. – lhf Apr 23 '18 at 23:48

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From Gallian's Contemporary abstract algebra:

The term "homomorphism" comes from the Greek words homo,"like", and morphe,"form". The concept of group homomorphism was introduced by Camille Jordan in $1870$, in his influenced book "Traite des substitutions"

Addition: The Treatise embodied the substance of most of Jordan’s publications on groups up to that time (he wrote over 30 articles on groups during the period 1860—1880) and directed attention to a large number of difficult problems, introducing many fundamental concepts. For example, he made explicit the notions of isomorphism and homomorphism for (substitution) groups

Although this book and this might help!

Chinnapparaj R
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