The terminology "homomorphism" and "homomorphic" in group theory emerged through a shift from earlier conventions, particularly those established by Camille Jordan. Here's a breakdown of the earliest known occurrences based on available historical records:

"Homomorphic" (Adjective)

The term "homomorphes" (French, "homomorphic") first appears in the context of group theory in Jean de Séguier...

Short answer: no. Both the word and the modern separation of “isomorphism” vs “homomorphism” are older than the examples you list and were in circulation already in the 1890s, first in the algebra-of-logic/universal-algebra literature and, on the group-theory side, in German algebra.

What changed

• In Jordan (1870) and much of the 19th‑century group literature, “isomorphism” covered what we would...

(The dates are those of the printed sources; page–numbers are given so that the quotations can be checked in the scans that are freely available on-line.)

1. Where does the word come from?
   The adjective homomorphos (ὁμόμορφος = “of the same shape”) is classical Greek and had been used in the nineteenth century, especially in biology.
   When mathematicians looked for a name for the relati...

This is an excellent question about the evolution of mathematical terminology. The shift from Jordan's usage (where "isomorphism" meant what we now call "homomorphism") to modern terminology appears to have occurred gradually in the early 20th century.

Early History

Jordan's terminology (1870) indeed used:

• "isomorphisme" for what we now call homomorphism
• "isomorphisme holoédrique" (holoed...

This is an excellent question that points to a crucial transition in the language and conceptual framework of abstract algebra. The shift from Jordan's terminology to the modern one was not instantaneous but happened over several decades, driven by a need for greater precision and a fundamental change in perspective from studying groups as collections of substitutions to studying algebraic structu...

Hmm, this seems like a deep dive into mathematical etymology. The user is clearly well-versed in the subject - they're citing obscure 19th century texts ...

History of the Terms "Homomorphism" and "Homomorphic" in Algebra

Based on the references you've provided and my knowledge of mathematical history, I can offer some insight into the evolution of these terms, though I can't definitively state these are the earliest occurrences without a more exhaustive search.

Historical Development

The etymology suggests why these terms were chosen: from Gr...

Below is (1) the first occurrences that I have been able to locate of homomorphe, Homomorphismus, homomorphic, homomorphism, and (2) a short explanation of why the word was introduced and how it replaced Jordan’s earlier terminology.

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1. The earliest occurrences that can be traced ────────────────────────────────

All dates are publication dates; the passages can ...

Here is what one finds if one pushes back through the old German and French literature:

1. Jordan (1870) himself had only two names in his Traité des substitutions:
   – “isomorphisme” for any correspondence preserving the group‐law (not necessarily one‐to‐one)
   – “iso­holoédrique” (holoëdric) for the bijective case.
   Thus in Jordan’s language our modern “homomorphism” was calle...