Finite and infinite group

In summary, an infinite group that has exactly two elements with order 4 is a subset of the complex numbers where the multiples of the imaginary unit, i, have an order of 4.
  • #1
tim656
1
0
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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  • #2
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 ?
 

1. What is a finite group?

A finite group is a group that has a finite number of elements. This means that there is a specific, limited number of elements that belong to the group and can be combined using the group operation.

2. What is an infinite group?

An infinite group is a group that has an infinite number of elements. This means that there is no limit to the number of elements that belong to the group and can be combined using the group operation.

3. What are some examples of finite groups?

Some examples of finite groups include the group of integers modulo n, the group of symmetries of a regular polygon, and the group of permutations of a set with n elements.

4. What are some examples of infinite groups?

Some examples of infinite groups include the group of real numbers under addition, the group of rational numbers under addition, and the group of complex numbers under multiplication.

5. What is the significance of finite and infinite groups in science?

Finite and infinite groups are important in various fields of science, such as mathematics, physics, and chemistry. They are used to study the symmetries and patterns in nature, and to describe and analyze complex systems and structures. They also have applications in cryptography, coding theory, and other areas of computer science.

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