noun
pronunciation:
[ gro͞op ˌhōməˈmôrˌfizəm ]
meaning:
given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that
where the group operation on the left hand side of the equation is that of G and on the right hand side that of H.
From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H,
and it also maps inverses to inverses in the sense that
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