anonymous
  • anonymous
Prove that O(G) mod O(H) =0 ??? Well i'm guessing that i have somehow to use the lagrange theorem to prove the above but am not too sure how to apply it any help will be greatly appreciated thanks :).
Algebra
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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AmTran_Bus
  • AmTran_Bus
@.Sam. @DLS @Eleven17 @jdoe0001 @Jhannybean @jhonyy9 @nubeer @phi
zzr0ck3r
  • zzr0ck3r
um, what is G and H?
zzr0ck3r
  • zzr0ck3r
are these sets or groups? is this number theory, set theory, or group theory?

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zzr0ck3r
  • zzr0ck3r
@Stephane1200
anonymous
  • anonymous
Sorry for the delayed reply, well G would be the group and H a subgroup.
zzr0ck3r
  • zzr0ck3r
ok so G is a group C is a subgroup then ord(C) | ord(G)
zzr0ck3r
  • zzr0ck3r
thus ord(G) modulo ord(C) = 0 i.e there is no remainder when we divide ord(G) with ord(C)
zzr0ck3r
  • zzr0ck3r
and yes this is lagrange theorem.
zzr0ck3r
  • zzr0ck3r
we are assuming G is finite....
zzr0ck3r
  • zzr0ck3r
@Stephane1200 understand?
anonymous
  • anonymous
Ok i think i get what you mean so basically i can use euclid principle to prove the above...
zzr0ck3r
  • zzr0ck3r
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
zzr0ck3r
  • zzr0ck3r
I forget what Euclid principle is...sec
anonymous
  • anonymous
oh sorry my bad
zzr0ck3r
  • zzr0ck3r
is that not dealing with geometry?
anonymous
  • anonymous
you are right from definition
zzr0ck3r
  • zzr0ck3r
ok :)
anonymous
  • anonymous
if H is a subgroup of G then order of H should divide that of G
zzr0ck3r
  • zzr0ck3r
will divide*
anonymous
  • anonymous
lol yh will divide :P
anonymous
  • anonymous
hence if it divides there's no remainder the reason why it is zero ?
zzr0ck3r
  • zzr0ck3r
yeah 8mod2=0 8mod3=2 7mod6=1 it gives the remainder
zzr0ck3r
  • zzr0ck3r
9mod18=9
anonymous
  • anonymous
hmmm with examples it got easier now :)
zzr0ck3r
  • zzr0ck3r
have you done number theory?
anonymous
  • anonymous
well we covered it a bit
anonymous
  • anonymous
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
zzr0ck3r
  • zzr0ck3r
yeah, I doupt you need to learn the proof, but its easy. Just know the theorem.
zzr0ck3r
  • zzr0ck3r
p.s. definitions are man made, theorems are just true(if proved).
anonymous
  • anonymous
lol i already learned the proof and it's quite long xD
zzr0ck3r
  • zzr0ck3r
its easy with cosets:)
anonymous
  • anonymous
yh cosets are easy :)
anonymous
  • anonymous
looks like you already did abstract algebra :p
zzr0ck3r
  • zzr0ck3r
im in it now:)
zzr0ck3r
  • zzr0ck3r
but done with number theory, and your question was more number theory.
anonymous
  • anonymous
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
anonymous
  • anonymous
have you already done ring and field

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