Difference between revisions of "Isomorphism"
From Conservapedia
(New page: Given two groups <math>G,G'</math>, an '''isomorphism''' from <math>G</math> to <math>G'</math> is a function <math>\phi : G \to G'\,</math> such that <math>\phi</math> is a [[homo...) |
|||
| Line 1: | Line 1: | ||
| − | Given two [[group]]s <math>G,G'</math>, an '''isomorphism''' from <math>G</math> to <math>G'</math> is a [[function]] <math>\phi : G \to G'\,</math> such that <math>\phi</math> is a [[homomorphism]] and <math>\phi</math> is [[bijective]]. | + | Given two [[group]]s <math>G,G'</math>, an '''isomorphism''' from <math>G</math> to <math>G'</math> is a [[function]] <math>\phi : G \to G'\,</math> such that <math>\phi</math> is a [[homomorphism]] and <math>\phi</math> is [[bijective]].<br /><br /> |
| + | Two groups <math>G,G'</math> are called '''isomorphic''' if an isomorphism from <math>G</math> to <math>G'</math> exists. | ||
<!--Apologies if the TeX and font size don't work well together. I have Firefox set to use a specified font to avoid a weird bug, so I'm not sure how it'll look normally. - CSGuy --> | <!--Apologies if the TeX and font size don't work well together. I have Firefox set to use a specified font to avoid a weird bug, so I'm not sure how it'll look normally. - CSGuy --> | ||
[[Category:Algebra]] | [[Category:Algebra]] | ||
Revision as of 23:31, November 29, 2007
Given two groups 
, an isomorphism from 
to 
is a function 
such that 
is a homomorphism and is bijective.
Two groups are called isomorphic if an isomorphism from to exists.
