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ehrenfest
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[SOLVED] group theory problem
A cyclic group of order 15 has an element x such that the set {x^3,x^5,x^9} has exactly two elements. The number of elements in the set {x^{13n} : n is a positive integer} is
a)3
b)5
From the given information, we know that x^6 = 1 or x^4 = 1. In the first case, either answer is possible. In the second case, only answer a is possible. Anyway, do we know enough to decide which case this is or is there a different way to do the problem?
Homework Statement
A cyclic group of order 15 has an element x such that the set {x^3,x^5,x^9} has exactly two elements. The number of elements in the set {x^{13n} : n is a positive integer} is
a)3
b)5
Homework Equations
The Attempt at a Solution
From the given information, we know that x^6 = 1 or x^4 = 1. In the first case, either answer is possible. In the second case, only answer a is possible. Anyway, do we know enough to decide which case this is or is there a different way to do the problem?