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Let x belong to a group. If x2 e and x6 = e, prove that x4
Chapter 3, Problem 20E(choose chapter or problem)
QUESTION:
Let x belong to a group. If \(x^2 \neq e\) and \(x^6 = e\), prove that \(x^4 \neq e\) and \(x^5 \neq e\). What can we say about the order of x?
Questions & Answers
QUESTION:
Let x belong to a group. If \(x^2 \neq e\) and \(x^6 = e\), prove that \(x^4 \neq e\) and \(x^5 \neq e\). What can we say about the order of x?
ANSWER:Step 1 of 4
Consider an element that belongs to a group . Here, it is given that and .