What Is an Infinite Group with Exactly Two Elements of Order 4?

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An infinite group with exactly two elements of order 4 is being sought in the discussion. The user suggests using the group of units under multiplication modulo 5, specifically focusing on the elements 2 and 3, which both have order 4. Another participant hints at considering subsets of the complex numbers, particularly the multiples of the imaginary unit, i, as a potential solution. The conversation revolves around identifying the correct infinite group structure that meets the specified criteria. Further exploration and clarification are encouraged to refine the answer.
tim656
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what is an infinite group that has exactly two elements with order 4?

i let G be an infinite group for all R_5 ( multiplication modulo 5) within this interval [1,7)
so i got |2|=|3|=4.

i'm not sure this is the right answer but i couldn't think of anything else at a moment. help please.
 
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tim656 said:
what is an infinite group that has exactly two elements with order 4?

i let G be an infinite group for all R_5 ( multiplication modulo 5) within this interval [1,7)
so i got |2|=|3|=4.

I'm not sure this is the right answer but i couldn't think of anything else at a moment. help please.
Hello tim656. Welcome to PF !

Think about some subset of the complex numbers.

What are the multiples of the imaginary unit, i ?
 

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