need to prove that for a group with only one element from Order 2, this element belong to the center of the group, how to prove that?
A group with only one element from Order 2
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group-theory
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1What on earth does "organ" mean here? – 2017-02-20
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0I think you meant 'element' instead of 'organ'. But still !!! – 2017-02-20
1 Answers
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Hint: Let $G$ be a group with a unique $\sigma$ of order $2$, and let $g \in G$ be arbitrary. What is the order of $g\sigma g^{-1}$?