OpenStudy (swissgirl):

Show that any 2 groups of order 2 are isomorphic

6 years ago
OpenStudy (kinggeorge):

I've got 5 minutes. Basically, you want to take two generic order two group such as \(\{\{a,b\},*_1\}\) and \(\{\{c,d\},*_2\}\) where \(a\) and \(c\) are the respective identities.

6 years ago
OpenStudy (kinggeorge):

If you show an isomorphism between these, it'll be enough for any 2 groups since these were chosen arbitrarily.

6 years ago
OpenStudy (swissgirl):

what the heck is an isomorphism though? Like I am not sure i get how to prove it

6 years ago
OpenStudy (kinggeorge):

Given a function \(\varphi\), you need to show that \[\varphi(g*h)=\varphi(g)\cdot\varphi(h)\]and that \(\varphi\) is bijective.

6 years ago
OpenStudy (swissgirl):

ohhhhhhh

6 years ago
OpenStudy (kinggeorge):

Sorry, got to go now. I'm super busy :( Good luck.

6 years ago
OpenStudy (swissgirl):

THANKKSSSS

6 years ago
OpenStudy (kinggeorge):

You're welcome.

6 years ago