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@.Sam. @DLS @Eleven17 @jdoe0001 @Jhannybean @jhonyy9 @nubeer @phi
um, what is G and H?
are these sets or groups? is this number theory, set theory, or group theory?
Sorry for the delayed reply, well G would be the group and H a subgroup.
ok so G is a group C is a subgroup then ord(C) | ord(G)
thus ord(G) modulo ord(C) = 0 i.e there is no remainder when we divide ord(G) with ord(C)
and yes this is lagrange theorem.
we are assuming G is finite....
Ok i think i get what you mean so basically i can use euclid principle to prove the above...
hmm, Lagrange theorem says if G has finite order and H belongs to G, then |h| | |g| and since a | b b mod a = 0
I forget what Euclid principle is...sec
oh sorry my bad
is that not dealing with geometry?
you are right from definition
if H is a subgroup of G then order of H should divide that of G
lol yh will divide :P
hence if it divides there's no remainder the reason why it is zero ?
yeah 8mod2=0 8mod3=2 7mod6=1 it gives the remainder
hmmm with examples it got easier now :)
have you done number theory?
well we covered it a bit
thx dude now i figured out i will have to use the lagrange theorem maybe not the full proof but at least the definition to demonstrate the claim that O(G) mod O(H) =0
yeah, I doupt you need to learn the proof, but its easy. Just know the theorem.
p.s. definitions are man made, theorems are just true(if proved).
lol i already learned the proof and it's quite long xD
its easy with cosets:)
yh cosets are easy :)
looks like you already did abstract algebra :p
im in it now:)
but done with number theory, and your question was more number theory.
oh ok i see well i was rounding up the bits and pieces i don't really know given i have exams in that on monday :P
have you already done ring and field