- #1
jimmycricket
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Homework Statement
For a group [itex]G[/itex] consider the map [itex]i:G\rightarrow G , i(g)=g^{-1}[/itex]
For a subgroup [itex]H\subset G[/itex] show that [itex]i(gH)=Hg^{-1}[/itex] and [itex]i(Hg)=g^{-1}H[/itex]
Homework Equations
The Attempt at a Solution
I know that for [itex] g_1,g_2 \in G[/itex] we have [itex]i(g_1g_2)=(g_1g_2)^{-1}=g_2^{-1}g_1^{-1}[/itex]
Then since for any [itex]h\in H, h\in G [/itex] we have [itex]i(g_1h)=(g_1h)^{-1}=h^{-1}g_1^{-1}[/itex]
Is this a good approach to the problem?