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When was the concept of a "homomorphism" of algebraic structures first introduced?

Steinitz' 1910 paper Algebraic Theory of Fields is often pointed to as the first true work of abstract algebra, yet the concept of homomorphism is lacking in this work. For example, here is Steinitz' definition of isomorphism (page 172):

Two systems $\frak{S}_1$, $\frak{S}_2$ with double composition are called isomorphic or from the same (composition) type if it is possible to relate their elements unambiguously to one another, so that to the sum and product of any two elements of one system is assigned every time the sum and the product of the corresponding elements in the other; the relation itself is called an isomorph or isomorphism.

This definition seems clumsy by modern standards. I'm wondering who improved it and when.

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  • $\begingroup$ I'll just mention that the tag (abstract-algebra) is deprecated (see the tag-info) for more details. If it's possible, it might be useful to find other suitable tags. $\endgroup$
    – Martin Sleziak
    Commented Aug 1, 2018 at 18:07

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The word "homomorphism" in English appears in 1935, at least that is the earliest listed by the Oxford English Dictionary.

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    $\begingroup$ That’s a rather crude upper bound! $\endgroup$
    – Piotr Achinger
    Commented Aug 1, 2018 at 17:45
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    $\begingroup$ According to the question at mathoverflow.net/questions/280261/…, Jordan (I assume Camille Jordan) wrote about homomorphisms in 1870 (but called them "isomorphisms"), so the concept is at least 65 years older than the OED citation. $\endgroup$
    – Sophie Swett
    Commented Aug 1, 2018 at 17:49
  • $\begingroup$ That question seems close enough for this to be a duplicate. I'm voting to close the question. $\endgroup$
    – Timothy Chow
    Commented Aug 2, 2018 at 1:40

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