Purchase Solution

Groups and Integers

Not what you're looking for?

Ask Custom Question

Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n).

Purchase this Solution
Solution Summary

A proof involving groups and integers is provided. the proof is concise.

Solution Preview

E should mean 1 in S_n.
Proof: We know each permutation can be expressed as a product of some non-intersection cycles, where the length of the cycle is less than or equal to ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

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

Solving quadratic inequalities

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

View More Free Quizzes
Related BrainMass Solutions

  • Element of Finite Order

    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).

  • Problems in Group Theory

    455433 Problems in Group Theory: Homomorphism Let G_1 and G_2 be groups and ?:G_1?G_2 a map. Which of the following is a group homomorphism? Explain your answers. If ? is a homomorphism, describe the kernel and the image of ?. a) G_1=C_4=?

  • Analysis of Cyclic Groups

    Cyclic groups and their relationship to the group of integers under the operation addition is explained in detail, including looking at the structure of their subgroups and factor (or quotient) groups.

  • Basic Groups - Positive integers

    295924 Basic Groups - Positive integers For any integer n > 2, show that there are at least two elements in U(n) that satisfy x^2 = 1 Note: For each n > 1, we define U(n) to be the set of all positive integers less than n and relatively prime to

  • Facts About Group Theory

    There are finite and infinite cyclic groups. All infinite cyclic groups are isomorphic to the additive group of integers. All cyclic groups of an order n are isomorphic to the additive group of integers Z_n modulo n .

  • Infinite Groups

    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 Q/Z is an infinite group.

  • R-modules

    Identify Hom(Z/nZ,Z), Hom(Z,Z/nZ), Hom(Z/3Z,Z/6Z), Hom(Z/10Z,Z/6Z) as abelian groups, where n belongs to Z and Z is the set of integers. Please see the attachment.

  • Discrete Math : Numbers of Solutions to Equations

    57841 Discrete Math : Numbers of Solutions to Equations A) Let n and r be positive integers.

  • Factor Group and Torsion Group

    Factor Groups and Torsion Groups are investigated. The solution is detailed and well presented.

View More Related Solutions