Question

If H is a subgroup of G, are there any cosets gH of H in G that exist? Besides H=1H.

Answer 1

so long as g has an inverse in H, then gH should be a subgroup.

Answer 2

however, gH will be the same subgroup as 1H.

Answer 3

THAT"S WHAT I THOUGHT!!! Thank you so much!!!!!!

Answer 4

you're welcome! yeah, gH would just be a permutation of H, provided gH is a subgroup.

Answer 5

that's what I thought but the way the professsor asked the question got me all confused. I really can't believe I figured that out on my own for once and that someone's answer corresponded with mine. Thanks so much

Answer 6

kudos to you!!!