g²=Ifor all h is an element of H.

a)Prove: H is an abelian group

b)Prove: Suppose |H|<∞.Let {h₁,h₂,…..hn} be minimal set of generators for H. then http://www.mathhelpforum.com/math-he...2647988b-1.gif

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- Nov 5th 2009, 05:51 PMapple2009prove H is an abelian group
g²=

*I*for all h is an element of H.

a)Prove: H is an abelian group

b)Prove: Suppose |H|<**∞.**Let {h₁,h₂,…..hn} be minimal set of generators for H. then http://www.mathhelpforum.com/math-he...2647988b-1.gif - Nov 5th 2009, 06:17 PMDrexel28
: Suppose $\displaystyle G$ is a group such that $\displaystyle g^2=e_G\quad\forall g\in G$. Prove that $\displaystyle G$ is abelian.**Problem**

Note that $\displaystyle g^2=e\implies g=g^{-1}$. Therefore $\displaystyle \left(ab\right)=\left(ab\right)^{-1}=b^{-1}a^{-1}=ba$.**Proof (1):**

Using the above we can see that $\displaystyle ab=a\left(e_G\right)b=a(ab)^2b=(aa)ba(bb)=a^2bab^2 =ba$**Proof (2):**

Part b doesn't make sense. Is there a typo? - Nov 5th 2009, 06:41 PMDrexel28