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## Main Question or Discussion Point

G group, H subgroup of G.

Suppose aH and bH are distinct leftcosets then Ha and Hb must be distinct right cosets?

My humble thoughts:

the left coset aH consists of a times everything in H;

Ha consists of everything in H times a.

Then this argument above is true?

Suppose aH and bH are distinct leftcosets then Ha and Hb must be distinct right cosets?

My humble thoughts:

the left coset aH consists of a times everything in H;

Ha consists of everything in H times a.

Then this argument above is true?