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cosets of a subgroup

Name: EFG 2007-10-19 14:21

Halp me please !

I need to prove that two cosets aH, bH of a subgroup H of group G are either identical or disjoint.

can someone point me in the right direction ?

Name: Anonymous 2007-10-22 23:47

Definitions than contradiction?

Name: Anonymous 2007-10-23 0:00

if h1,h2 \in H and a*h1 = b*h2, then

a = b*h2*h1^-1 \in bH

implies aH \subset bH

Name: Anonymous 2007-10-23 1:19

>>1
you don't need to if you take biology

There's srysly some hot girls there

Name: Anonymous 2007-10-23 9:19

You have aH. If b is in aH then bH = aH. Else bH /= aH.

Name: Anonymous 2007-10-24 3:08

>>5
Disjoint and non-equal are not the same thing, dipshit. The entire point of the question is to show that bH /= aH implies bH is disjoint from aH.

Name: Anonymous 2007-10-24 11:17

>>1
Did this last year in Groups. I'll give you a direction. Assume that they're not identical, but not disjoint either, so that there is some element z in both aH and bH (and how can z therefore be written?). Your best bet now is to use this to show that aH is a subset of bH, and conversely bH is a subset of aH (what >>3 was getting at).

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