Group Theory

"Show that two different left cosets of G with respect to H have the same number of elements."

I don't seem to have any proof of this in my lecture notes but it is examinable, could someone please explain to me how I would approach such a proof?

Thank you!

Question

Group Theory

"Show that two different left cosets of G with respect to H have the same number of elements."

I don't seem to have any proof of this in my lecture notes but it is examinable, could someone please explain to me how I would approach such a proof?

Thank you!

anonymous · Answer

Can you give a bijective map from one coset to the other?

anonymous · Answer

see page 94 & 95

anonymous · Answer

Thankyou! This makes a lot of sense now :)

anonymous · Answer

you're welcome!

anonymous · Answer

http://www.millersville.edu/~bikenaga/abstract-algebra-1/coset/coset.html Here's a paper with a slightly different approach. It's under the lemma "Any two left cosets have the same number of elements."