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

[tim656]

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.

 

[SammyS]

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 ?