Today ***homomorphism*** (resp. *isomorphism*) means what Jordan ([1870](https://archive.org/stream/traitdessubsti00jorduoft#page/56)) had called *isomorphism* (resp. *[holoedric](https://hsm.stackexchange.com/questions/3108/jordan-called-isomorphisms-iso-and-homomorphisms-iso-holoedriques-and-iso) isomorphism*). How did the switch happen?


“Homomorphic” (and “homomorphism” as “property of being homomorphic”) are e.g. in de Séguier ([1904](https://www.emis.de/cgi-bin/JFM-item?36.0187.02), [pp. 65–66](https://archive.org/stream/thoriedesgroup00sguoft#page/65)) and the last edition of Weber ([1912](https://www.emis.de/cgi-bin/JFM-item?43.0143.01), [p. 195](https://books.google.com/books?id=5vDuAAAAMAAJ&pg=PA195&dq=Homomorphismus)). “Homomorphism” as map of groups is e.g. in Schur ([1924](https://www.emis.de/cgi-bin/JFM-item?50.0293.02), [p. 192](https://books.google.com/books?id=I_gY2dTnDXwC&dq=Homomorphismus)). But none of these sound like a first.


I asked this on [hsm](https://hsm.stackexchange.com/questions/6460/whence-homomorphism-homomorphic) a week ago, but got no answer there.



Whence “homomorphism” and “homomorphic”?
I found this footnote on page 195 of Fricke and Klein's [Vorlesungen über die Theorie der automorphen Functionen](https://archive.org/details/vorlesungenber01fricuoft) (1897):


![](https://ilorentz.org/beenakker/MO/Fricke_Klein.png)


Translation:



> 
> The term "homomorphic" seems more appropriate than the previously$^\ast$ used "isomorphic", because it refers not to "equality" but to "similarity" of two groups. The term "isomorphism" will therefore from now on be used in the sense of "1-to-1 homomorphism".
> 
> 
> 


$^\*$l.c. = loco citato — this seems to refer to Fricke and Klein's [Vorlesungen über die Theorie der elliptischen Modulfunctionen](https://books.google.com/books?id=2ZQLAAAAYAAJ&pg=PA138&dq=Isomorphismus) (1890).


