Difference between revisions of "Isomorphism"
Jump to navigation
Jump to search
DavidB4-bot (talk | contribs) (clean up & uniformity) |
|||
| (4 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | Given two [[Group (mathematics)|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 [[Bijection|bijective]]. | |
| + | |||
| + | |||
Two groups <math>G,G'</math> are called '''isomorphic''' if an isomorphism from <math>G</math> to <math>G'</math> exists. | 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 --> | ||
| − | ==See | + | ==See also== |
*[[Automorphism]] | *[[Automorphism]] | ||
[[Category:Algebra]] | [[Category:Algebra]] | ||
Latest revision as of 14:29, July 13, 2016
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 homomorphism and <math>\phi</math> is bijective.
Two groups <math>G,G'</math> are called isomorphic if an isomorphism from <math>G</math> to <math>G'</math> exists.