well defined for me

[포트란77]

let H be a normal subgroup of a group G

show that G/H ={gH | g in G} is well defined by the equation

(aH)(bH) = (ab)H

----------------------------

next process is contents in algebra book by Fraleigh

choosing a in aH and b in bH ,we obtain the coset (ab)H.

choosing different representatives ah1 in aH and bh2 in bH,

we obtain the coset a(h1)b(h2)H

we must show that these are the same coset.

now, h1b in Hb = bH so (h1)b = b(h3) for some h3 in H

thus (ah1)(bh2) = a(h1b)h2 = a(bh3)h2 = (ab)(h3h2)

and (ab)(h3h2) in (ab)H

therefore, a(h1)b(h2) is in (ab)H

-------------------------------------

but my process is~~~~~

let aN = cN , bN = dN

thus c=a(h1) , d=b(h2) for some h1, h2 in H
(because aH = cH <=> (a^-1)c in H )

cdH = (a(h1)b(h2))H = (ab(h1)(h2))H = abH

thus well defined


이것도 맞는 말인가요??

[허걱~]

네 맞는 말이네요 -_-;;

[포트란77]

아고...H를 N으로 잘못썼네요. 하여튼 맞긴 맞나보죠??