abstract algebra

[regula_rationis]

Why is any left coset of a subgroup H equal to a right coset of some subgroup not necessarily H?

Comments

[phlebas]

...or a suitably chosen g.

[regula_rationis]

You're saying the identity of the group always works?

[phlebas]

The identity would be one example, yes. I was just clarifying that finding some g such that H = gHg-1 does not mean the subgroup is normal - the subgroup is only normal if that is true for any choice of g.