Suppose that G is an Abelian group with an odd number of elements. show that the product of all the elements of G is the identity.

Let |G|=8. Show that G must have and element of order 2.

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- Oct 16th 2008, 06:38 PMJuancd08Lagrange Theorem.
Suppose that G is an Abelian group with an odd number of elements. show that the product of all the elements of G is the identity.

Let |G|=8. Show that G must have and element of order 2. - Oct 16th 2008, 07:04 PMThePerfectHacker
Hint: Pair $\displaystyle x$ and $\displaystyle y$ so that $\displaystyle xy=e$. Note why you need the fact that $\displaystyle |G|$ is odd.

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Let |G|=8. Show that G must have and element of order 2.