Purchase Solution

Prove that every element of a susbet is of finite order.

Not what you're looking for?

Ask Custom Question

Let G= , x*y be the fractional part of x+y .(i.e:x*y=x+y-[x+y] where
[a] is the greatest integer less than or equal than a).
Show that all the elements of the subset of all rational elements of this group are of finite order.

Please see the attached file for the fully formatted problems.

Attachments
Purchase this Solution
Solution Summary

It is proven that every element of a susbet is of finite order. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Let G= , x*y be the fractional part of x+y .(i.e:x*y=x+y-[x+y] where
[a] is the greatest integer less than or equal than ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Infinite Groups

    Find examples of the following: an infinite group such that every element has finite order. An example is the quotient group Q/Z with the group operation addition "+". We will prove that every element of Q/Z has finite order. Proof.

  • Element of Finite Order

    11893 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. First of all, the group operation here is addition.

  • Subgroup

    Let G be a finite group in which every element has a square root; that is, for each x in G, there exists y in G with y=x2. Prove that every element in G has a unique square root. 6.

  • Group theory

    Done (b) Prove that if G is a finite group, H subset of G that is closed with respect to the operation of G, Then every element of H has its inverse in H. We can use the result of (a).

  • Binary Operations : Idempotence

    12811 Binary Operations : Idempotence An element e of a monoid M is called an idempotent if e^2 = e. If M is finite, show that some positive power of every element is an idempotent.

  • Euclidean Algorithm

    Use the following definition of the order of an element in a finite group : The order of an element g in a finite group G is the least positive integer n such that gn=1. 5. 6. 7. 8. 9.

  • Homomorphisms and Surjections

    97971 Homomorphisms and Surjections Let f:G->H be a group homomorphism. Prove or disprove the following statement. 1.Let a be an element of G. If f(a) is of finite order, then a is also of finite order. 2.Let f be a surjection.

  • Partial order proof

    a) prove that S is finite, then xRy for all s in S b) show that the conclusion in (a) need not be true if S is infinite Proof: (a) For any y in S, since R is a partial order on S, then if y is not a minimal element in S, we can find y1 in S, such that

  • Groups and Distinct Elements

    93981 Groups and Distinct Elements Let G be a group and let be two distinct elements. Let n be the order of g and m be the order of h. Prove or disprove that there is no pair i,j , such that .

View More Related Solutions