Let H be subgroup of abelian group G, then show that:

i) $\displaystyle (aH)^-1=a^-1H$

ii) $\displaystyle (Ha)^2=Ha^2$

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- Oct 21st 2009, 10:33 AMGTK X Huntershow that...
Let H be subgroup of abelian group G, then show that:

i) $\displaystyle (aH)^-1=a^-1H$

ii) $\displaystyle (Ha)^2=Ha^2$ - Oct 21st 2009, 03:42 PMaman_cc
- Oct 21st 2009, 08:21 PMtonio
- Mar 27th 2010, 12:55 AMGTK X Hunter
take any $\displaystyle h\in H$

i) $\displaystyle (ah)^{-1}=h^{-1}a^{-1}=a^{-1}h^{-1}=a^{-1}h_o$

ii) $\displaystyle haha=hhaa=h_1a^2$

am i right? ^_^ - Mar 27th 2010, 12:41 PMDrexel28