Element of Finite Order
Prove that every element of Q/Z has finite order, where Q is the set of rational numbers with group operation + and Z is the set of integers.
© BrainMass Inc. brainmass.com June 7, 2023, 2:27 pm ad1c9bdddfhttps://brainmass.com/math/combinatorics/element-finite-order-11893
Solution Preview
First of all, the group operation here is addition. Q is the set of rational numbers, Z the set of integers. Neither one of these sets is finite. There are an infinite number of integers and an infinite number of rational numbers (these do include the integers).
So it's not going to do any good to suppose for a minute that either of these groups has finite ...
Solution Summary
It is proven that every element of Q/Z has finite order, where Q is the set of rational numbers with group operation + and Z is the set of integers.
Free BrainMass Quizzes
-
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
-
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
-
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
-
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
-
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.