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Group homomorphism
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Group homomorphism
In mathematics, 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 Hence one can say that h "is compatible with the group structure".
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License: Creative Commons Attribution-Share Alike 3.0 (CC-BY-SA-3.0)
Author-Info: Cronholm144
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
Group homomorphism
In mathematics, 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 Hence one can say that h "is compatible with the group structure".
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC-BY-SA-3.0)
Author-Info: Cronholm144
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video