### Determine the number of elements

Assignment Help Mathematics
##### Reference no: EM131069898

1. Establish or each of the following statements as being true false. Justify each answer fully.

(a) Z5 ⊕ Z12 ≅ Z60

(b) Z5 ⊕ Z10 ≅ Z50

(c) Z12 ⊕ Z4 ≅ Z24 ⊕ Z2

(d) U(180) ≅ U(112)

2. (a) Express U(77) as an external direct product of groups of the form Zn in three different ways.

(b) Express Aut(Z55) as Zm ⊕ Zn for some m and n.

3. Suppose φ is an isomorphism from Z5 ⊕ Z11 to Z55, and φ(2, 3) = 4. Find the element that φ maps to 1.

4. Give an example of an infinite non-Abelian group with precisely six elements of finite order.

5. Find two (distinct) subgroups of order 30 in Z50 ⊕ Z60.

6. Determine the number of elements of order 10 and the number of cyclic subgroups of order 10 in Z20 ⊕ Z15.

#### Questions Cloud

 Cyclic compression loading normal to the plane of the notch : cyclic compression loading normal to the plane of the notch Pricincples underpinning skills development act : Examine the pricincples underpinning the Skills Development Act and the Skills Development Levies Act and discuss the implication of this for human resource planning in your organisation. (still Finland, Russia and SA assignment) Find the retirement calculator : Calculating Future Values - You have \$20,000 you want to invest for the next 40 years. You are offered an investment plan that will pay you 7 percent per year for the first 20 years and 11 percent per year for the last 20 years. Principles underpinning the skills development act : Examine the principles underpinning the Skills Development Act and Skills Development Levies Act and discuss the implication of this for human resource planning in your organisation. Determine the number of elements : Find two (distinct) subgroups of order 30 in Z50 ⊕ Z60. Determine the number of elements of order 10 and the number of cyclic subgroups of order 10 in Z20 ⊕ Z15 Issue of cultural stereotypes : Issue of cultural stereotypes. Discuss the following scenarios in relation to work and social lives: Select a country that interest you and research the following areas of communication: Bending specimen rotating at an angular velocity ? : Show that, in a bending specimen rotating at an angular velocity ω, the cyclic stress will be of the form ?σ = A sinωt, where A is the peak stress amplitude and t is the time. Principal theories of leadership and motivation : Explain the principal theories of leadership and motivation, and describe the fundamental considerations in managing and motivating individual and group behavior. Analysis of all information conveyed by a complete set : Explain how the analysis of all information conveyed by a complete set of financial statements enables an interested party to arrive at the most appropriate decisions about a business.

### Write a Review

#### What is the dependent and independent variable

What is the dependent and independent variable

#### The diameter of a car tire is 40cm and the diameter of a

the diameter of a car tire is 40cm and the diameter of a toy car tire is 18mm. find the ratio of the diameter of the

#### Inequality for the perimeter realted problems

The length of a rectangle is 5 mm longer than its width. Its perimeter is more than 30 mm. Let w equal the width of the rectangle.

#### Discrete math-structures

Make a meaningful example illustrating Project Evaluation and Review Technique (PERT). Explain all details. Draw the graphs involved. Use reasonable number of tasks.

#### How much work is needed to pump all of the water over side

A circular swimming pool has a diameter of 20 m, the sides are 4 m high, and the depth of the water is 3.5 m. How much work (in Joules) is required to pump all of the water over the side?

#### A man has a rectangular garden one length of the garden

a man has a rectangular garden. one length of the garden lies along a patio wall. however the rest of the garden is

#### What is the simulated value

a normal distribution has a mean of 500 a standard deviation of 50. A manager wants to simulate one value from this distribution, and has drawn the number 1.4 randomly. What is the simulated value?

#### In a survey of 8000 woman 5431 say they change their nail

in a survey of 8000 woman 5431 say they change their nail polish once a week. construct a 99 confidence interval for

#### Identify the current import policies

Conduct a search at GlobalEdge.msu.edu to identify the current import policies, tariffs and trade restrictions in FINLAND. Other useful sites include the World Trade Organization (www.wto.org). Enter FINLAND in the WTO search box (top right corner)..

#### Explain why those rates may be more meaningful

Explain why those rates may be more meaningful as a measure of change across time than the actual numbers of those events."

#### Express the hydrostatic force against one side

A triangle with base 1 m and height 3 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Give your answer correct to the nearest..

#### This is a transportation problem with all supplies and

question 1 a company has three new machines of different types. there are four different plants that could receive the