follow Dictionary.com

Stories We Like: A Guide to the Comma

automorphism

[aw-tuh-mawr-fiz-uh m] /ˌɔ təˈmɔr fɪz əm/
noun, Mathematics
1.
an isomorphism from a given set to itself.
Origin
1870-1875
1870-75; auto-1 + morph- + -ism
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
Cite This Source
Encyclopedia Article for automorphism

in mathematics, a correspondence that associates to every element in a set a unique element of the set (perhaps itself) and for which there is a companion correspondence, known as its inverse, such that one followed by the other produces the identity correspondence (I); i.e., the correspondence that associates every element with itself. In symbols, if f is the original correspondence and g is its inverse, then g(f(a))=I(a)=a=I(a)=f(g(a)) for every a in the set. Furthermore, operations such as addition and multiplication must be preserved; for example, f(a+b)=f(a)+f(b) and f(ab)=f(a)f(b) for every a and b in the set

Learn more about automorphism with a free trial on Britannica.com
Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
Cite This Source

Word of The Day

Difficulty index for automorphism

Few English speakers likely know this word

Word Value for automorphism

21
0
Scrabble Words With Friends