Meromorphic function: Difference between revisions

Revision as of 20:42, 24 December 2019

Revision as of 20:45, 24 December 2019

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==History==

The field of study where the term is used and the specific meaning of the term changed in the 20th&nbsp;century. In the 1930s, in [[group theory]], a ''meromorphic function'' (or ''meromorph'') was a function from a group ''G'' into itself that preserved the product on the group. The image of this function was called an ''automorphism'' of ''G''.<ref>{{cite book |last=Zassenhaus |first=Hans |author-link=Hans Zassenhaus |year=1937 |title=Lehrbuch der Gruppentheorie |publisher=B. G. Teubner Verlag |___location=Leipzig; Berlin |edition=1st |pages=29, 41}}</ref> Similarly, a ''homomorphic function'' (or ''homomorph'') was a function between groups that preserved the product, while a ''homomorphism'' was the image of a homomorph. This useform of the term is now obsolete, and the related term ''meromorph'' is no longer used in group theory.

The term ''endomorphism'' is now used for the function itself, with no special name given to the image of the function. The term ''meromorph'' is no longer used in group theory.

==Properties==