Monday, 19 August 2013

Prove that $ \pi_g $ is a permutation

Prove that $ \pi_g $ is a permutation

Suppose that $ G $ is group and $ g $ is any element from $ G $ ($g \in G
$). We define a function $ \pi_g : G \rightarrow G,\ \ \pi_g(x) = g \cdot
x$. Prove that $ \pi_g $ is a permutation of the set $ G $.
Could you show me how to prove this theorem? Thank for your help.

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