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\[H ^{*}=\left\{ xy ^{-1}:x,y \in H \right\}\le G\]

what the asterics H* means?

it sort of another H (it can be any later ie Q)

and by ≤ you mean that H* is a subset of G?

i mean it is a subgroup

by the way, which operation respect to is this an abelian group?

i gues multiplication?

1 H*\[\neq \]
2 let P,Q \[\in H ^{*}\]we want to show that PQ^-1 element H*

then PQ^-1 =\[(xy ^{-1})((xy ^{-1}))^{-1}\]

=\[(xy ^{-1})(x ^{-1}y)=(xx ^{-1})(yy ^{-1})\]

@terenzreignz pls help