# Suppose G is a group, a, b ∈ G such that |b| = 2 and bab = a^4 . [closed]

I know that answer is (2) |a| divides 15 but I'm not sure how they got the answer, any hints will be helpful thank you.

## closed as off-topic by Eevee Trainer, Jyrki Lahtonen, Jean-Claude Arbaut, Dietrich Burde, CesareoApr 22 at 9:35

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Hint: \begin{align}a^{16} &= (bab)^4\\ &= babbabbabbab \\ &= ba^4 b\\ &= b(bab)b \\ &= a.\end{align}