Question

Suppose that a is a group element and a^6=e. What are the posibilities for |a|? Provide reasons for your answer please.

Answer 1

the order of the element must divide 6

Answer 2

reasoning? if \(|a|=2\) i.e. \(a^2=e\) then \(a^6=(a^2)^3=e^3=e\)

Answer 3

similarly if \(a^3=e\) then \(a^6=e\)

Answer 4

i guess you should mention why this is impossible if \(|a|=4\) or \(5\)

Answer 5

thank you! That makes alot more sense now.