Suppose a and b are group elements and b e. If a–1ba = b2

Chapter 4, Problem 42SE

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Suppose a and b are group elements and \(b \neq e\). If \(a^{-1} b a=b^{2}\) and |a| = 3, find |b|. What is |b|, if |a| = 5? What can you say about |b| in the case where |a| = k?

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