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