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Who first used the word "homomorphism" to describe a link between two similar structures ? Following this, who specialized this concept with the words: - "Isomorphism"; - "Endomorphism"; - "Automorphism" ? Gérard Lang

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  • $\begingroup$ Yes, there is a possible duplicate concerning "homomorphism" and maybe also "isomorphism". But this is not the case concerning "endomorphism" and "automorphism", and it would be interesting to know when these different concepts have been neatly distinguished. $\endgroup$ – Gérard Lang Jan 11 '18 at 17:57
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    $\begingroup$ Since the question about the term "homomorphism" has been answered already, perhaps you can edit so that there is less overlap with the previous question. $\endgroup$ – j.c. Jan 11 '18 at 18:16
  • $\begingroup$ I accept the following answer for "Homomorphism" and "isomorphism" and will submit a separate question for "endomorphism " and automorphism. $\endgroup$ – Gérard Lang Jan 11 '18 at 22:34
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According to Jeff Miller's Earliest known uses of Some of the Words of Mathematics,

HOMOMORPHISM is found in English in 1935 in the Duke Mathematical Journal [OED].

A Google search for dates gives the same result.

UPDATE Thanks for your comments. After a more extended dates search, it appears that the word was in use in the mid 18th century, then disappeared from screens for more than 50 years!

This kind of search seems to output results dating back to 1869, but I stand a bit suspicious regarding what you get by clicking on them.

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    $\begingroup$ the word "homomorphism" is used casually in a sentence in that 1935 paper by S. Lefschetz, I cannot imagine this was the first time it appeared: There exists an operation $F$ defined topologically for all the chains and such that $F$ is a homomorphism... $\endgroup$ – Carlo Beenakker Jan 11 '18 at 18:11
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    $\begingroup$ See the question linked to above by Francois Ziegler for many earlier references mathoverflow.net/questions/280261 $\endgroup$ – j.c. Jan 11 '18 at 18:14
  • $\begingroup$ Why are you searching on the term in English instead of German? The people most intensively developing abstract algebra were in Germany. In a footnote on p. 319 of Bourbaki's book on set theory, they note that terms like "meriedric isomorphism" and "holoedric isomorphism" were in use up until Emmy Noether. See books.google.com/… $\endgroup$ – KConrad Jan 11 '18 at 18:54
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    $\begingroup$ Because of the earlier post by Ziegler, I think this post should be considered a duplicate question. $\endgroup$ – KConrad Jan 11 '18 at 18:57
  • $\begingroup$ Dear M. K Conrad, I already agreed that, without me knowing that, my question could partially be considered as duplicate; So, I can make a new question with the non-duplicate part. I also agree that I could have searched with the german term, but I thought that the usual language used in mathoverflow was english, so I used english. $\endgroup$ – Gérard Lang Jan 11 '18 at 22:26

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