411 REFERENCE · Wikibooks
Abstract Algebra/Group Theory/Homomorphism/Homomorphism Maps Identity to Identity
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Theorem
Let f be a homomorphism from group G to group K.
Let eG and eK be identities of G and K.
f(eG) = eK
Proof
{| Style = "width:75%;boarder:1px"
|-
| 0.
|| f maps to K
|-
| 1.
|| inverse in K
|-
| .
||
|-
| 2.
|| f is a homomorphism
|-
| 3.
|| identity eG
|-
| .
||
|-
| 4.
|| 1.
|-
| .
||
|-
| 5.
|| identity eK, definition of inverse
|-
| 6.
|| identity eK
|}