**Math 171: Abstract Algebra, Fall 2014- Assignment 2 **

1 Suppose G is a group and x, g ∈ G. Prove that the order of x and g^{-1}xg are the same. Deduce that the order of ab is the same as the order of ba for every a, b ∈ G.

2. Let G be a group. Determine whether or not each of the following must be a subgroup of G. If true, prove it. If false, give a counterexample:

(a) The set of elements of G that commute with every element in G. This is called the center of G and is denoted Z(G). That is,

Z(G) = {h ∈ G: gh = hg for all g ∈ G}.

(b) The set of elements of G that have finite order. That is, the set

H = {h ∈ G: |h| < ∞}.

3. Determine, with justification, all subgroups of (Z, +)

4. Which of the following subsets of D_{8} form a subgroup of D_{8}? Justify in each case.

(a) {1, r^{2}, s, sr^{2}}.

(b) {1, r^{2}, sr, sr^{3}}.

5. Read the "Generators and Relations" in Dummit & Foote, then prove for any n ≥ 3,

(r, s | r^{n} = s^{2} = 1, rsr = s).

is D_{2n}.

6. The Heisenberg group over a field F, denoted H(F), is the set of matrices defined by

(a) Prove that H(Z/pZ) is a non-abelian subgroup of GL_{3}(Z/pZ) for any prime p ≥ 2.

(b) Does H(R) have a non-identity element of finite order? Prove or disprove.

Explain the purpose of a swot analysis : Explain the purpose of a SWOT analysis. What are the alternatives? |

Survival after the government further cut their funding : The Colleges are facing issues of survival after the government further cut their funding. Two colleges have decided to merge to safeguard their provision and safeguard their staff jobs. List the major stakeholders that will be effected by the colleg.. |

Calculate the mass in milligrams of quinine in the tablet : Calculate the mass in milligrams of quinine in the tablet. |

Difference in decreasing costs-constant cost industry : The difference between a decreasing costs industry, a constant cost industry, and an increasing cost industry: Without relying on any algebra or geometry, differentiate the three types of industries. Give an example of an industry of each type and ex.. |

Prove that h is a non-abelian subgroup : Math 171: Abstract Algebra, Fall 2014- Assignment 2. Prove that H(Z/pZ) is a non-abelian subgroup of GL3(Z/pZ) for any prime p ≥ 2. Does H(R) have a non-identity element of finite order? Prove or disprove |

The stationary gaussian random sequence : The stationary Gaussian random sequence Xn has expected value E[Xn] = 0 and autocorrelation function RX [k] = cos(0.04πk). Use gaussvector to generate and plot 10 sample paths of the form X0,..., X99. What do you appear to observe? Confirm your su.. |

What is the square root : What is the square root of the 1521. once you have that answer, divide it by 13 and multiply it by 7. What would be your result? |

Method to reduce the risks of currency exchange : Your organization has always sold goods to the domestic market, for the first time they have expanded into Europe. As the Head of Internal Audit the board is concerned with risk of dealing with another currency (the Euro). The implications and risks .. |

Deals with constitutional issue : Find a Supreme Court case that deals with a constitutional issue (either pending or already decide d•Briefly describe the issue. Do you agree with the Court’s decision (or if it hasn’t been decided how do you think the case should be decided)? Why or.. |

## Find the volume of the volcanoA volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^14 and outside the cylinder x^2+y^2=1. Find the volume of the volcano. |

## In a class all pupils take mathematics m 18 take chemistryin a class all pupils take mathematics m 18 take chemistry c 17 take biology b and 24 take physics p of those taking 3 |

## Suppose youre tutoring a classmate in four algebraicimagine you are tutoring a classmate in the four algebraic processes. define each process and provide an example of |

## Explain what proportion of time does dr. smithWhat proportion of time does Dr. Smith eat a home lunch? d. If Taco Bell costs $3 and a home lunch costs $1 and the Springdale room is free, then how much lunch budget should he allow for his semester, which includes 100 lunches? |

## Find the possible dimensions of each corralyou have 240 feet of fencing to form two adjacent rectangular corrals. each coral has an area of 1000 square feet, find the possible dimensions of each corral. |

## Find the 90% coinfidence interval for the variancefind the 90%coinfidence interval for the variance and standard deviation for the time it takes an inspector to check a bus for the safety if a sample of 27 buses ha standard deviation of 6.8 minutes. Assume the variable is nornmally distributed. |

## What is the variance of the binomial distribution of votersWhat is the variance of the binomial distribution of voters supporting a particular referendum? In a survey, 80% of the voters support a particular referendum. If 20 voters are chosen at random |

## Determining compact subsetsDefine a new metric d on X = (0, 1/2)^2 by d((a,b), (r,s)) = 1 if a is not equal to r Or |b - s| if a = r. |

## Given that f(x)=x^2-20 and g(x)=15-x, find (f-g)(-3)Given that f(x)=x^2-20 and g(x)=15-x, find (f-g)(-3) if it exist |

## Compute the marginal revenue product at each level of laboruse the following data to answer the questions below. assume a perfectly competitive product market.units of |

## Solve the model using graphical analysisA restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products |

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd