Homomorphism

[hoh-muh-mawr-fiz-uh m, hom-uh-] /ˌhoʊ məˈmɔr fɪz əm, ˌhɒm ə-/

noun
1.
Biology. correspondence in form or external appearance but not in type of structure or origin.
2.
Botany. possession of perfect flowers of only one kind.
3.
Zoology. resemblance between the young and the adult.
4.
Mathematics. an into map between two sets that preserves relations between elements.
/ˌhəʊməʊˈmɔːfɪzəm; ˌhɒm-/
noun
1.
(biology) similarity in form
homomorphism
(hō’mə-môr’fĭz’əm, hŏm’ə-)
A transformation of one set into another that preserves in the second set the operations between the members of the first set.

mathematics
A map f between groups A and B is a homomorphism of A into B if
f(a1 * a2) = f(a1) * f(a2) for all a1, a2 in A.
where the *s are the respective group operations.
(2009-01-14)

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