Question

Show that any 2 groups of order 2 are isomorphic

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

ohhhhhhh

Answer 6

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

Good luck.

Answer 7

THANKKSSSS

Answer 8

You're welcome.