Purchase Solution

Abstract Algebra : Abelian Groups, Cauchy's Theorem, LaGrange's Theorem and Sylow Subgroups

Not what you're looking for?

Ask Custom Question

Let G be a nonabelian group of order 6. Show carefully that G must contain three elements of period 2 and two elements of period 3.

Let G be an abelian group of order 2n where n is odd. Determine how many elements of period 2 are contained in G. Fact: G must contain at least one element of period 2 (assume).

Attachments
Purchase this Solution
Solution Summary

Abelian Groups, Cauchy's Theorem, LaGrange's Theorem and Sylow Subgroups are investigated.

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

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.

Graphs and Functions

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

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Sylow p-Subgroups, Conjugacy and Abelian Groups

    99725 Sylow p-Subgroups, Conjugacy and Abelian Groups A) Let G be a group of order 203. Prove that if H is normal subgroup of order 7 in G then H<=Z(G). Deduce that G is abelian in this case.

  • Sylow's Theorem

    Modern Algebra Group Theory (CX) Sylow's Theorem Find all 3-Sylow subgroups of or, Sylow 3-subgroups and 2-Sylow subgroup or, Sylow 2-subgroups of the

  • Structure of Groups : Cauchy's Theorem, Order, Abelian Groups, Non-Abelian Groups, Isomorphisms and Subgroups

    50383 Structure of Groups : Cauchy's Theorem, Order, Abelian Groups, Non-Abelian Groups, Isomorphisms and Subgroups Let G be any non-Abelian group of order 6. By Cauchy's theorem, G has an element, a, of order 2.

  • Group Theory : Symmetry Groups, Cyclic Subgroups and Permutations

    Symmetry Groups, Cyclic Subgroups and Permutations are investigated. The solution is detailed and well presented.

  • Proof that There Are No Simple Groups of Order 56 or 148

    Now G can only be simple if it has 7 Sylow-2 subgroups and 8 Sylow-7 subgroups. We know from Sylow's second theorem that all Sylow-p subgroups are conjugate. In particular, all eight Sylow-7 subgroups must be conjugate.

  • Sylow theorem

    361467 Normal Sylow Theorem Let G be a group of order 48. By the 1st Sylow theorem G has a Sylow 2-subgroup and a Sylow 3-subgroup. Suppose none of these are normal. Determine the number of Sylow 2-subgroups and Sylow 3-subgroups that G can have.

  • Subgroup proofsno

    This is a series of proofs regarding groups and subgroups.

  • Two questions in group theory

    Thus and the isomorphism theorem gives us The solution comprises approximately 2 pages written in Word with mathematical notation written using Mathtype. Each step is explained, but assumes some background knowledge in abstract algebra.

  • Sylow's Theorem

    387631 Clarification of Sylow's Theorem A) Prove there is no simple group of order 200. b) Assume that a group G has two Sylow p-subgroups K and H. Prove that K and H are isomorphic.

View More Related Solutions