Proof that Let X = { a i| i I| be a set. Then the free

Question:

Proof that Let X = { a_i|i ϵ I| be a set. Then the free abelian group on X is (isomorphic to) the group defined by the generators X and the relations (in multiplicative notation) { a_ia_ja_i^-1a_j^-1 = e| i,j ϵ I}.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

See More Books

Question Posted: Apr 14, 2023 12:06 PM

See More Questions

Read "Environment pollution" and write a paper on it
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. F(x, y) = y i + x X j
The group defined by generators a, b and relations a n = e (3 n N*), b 2 = e and abab = e is the dihedral group D n . [See Theorem 6.13.] Theorem 6.13 For each n 3 the dihedral group D n is a...
Provide a brief description of the seven basic steps to use JDBC.
Sudoku Company issues 7,000 shares of $7 par value common stock in exchange for land and a building. The land is valued at $45,000 and the building at $85,000. Prepare the journal entry to record...
What measures can be implemented to combat the proliferation of illicit trade networks and transnational criminal organizations in an era of globalization ?
Figure 16.20 shows a system designed to recover argon from the purge stream in an ammonia synthesis plant. Estimate the total bare-module cost associated with the addition of this argon recovery...
An incomplete cost of goods manufactured schedule is presented below. InstructionsComplete the cost of goods manufactured schedule for Cepeda Manufacturing Company. CEPEDA MANUFACTURING COMPANY Cost...
5. Convert the following E/R diagrams to a relational database using the straight-E/R method. (a) length title to Stars year genre Movies Voices isa isa Cartoons Murder- Mysteries weapon
Given the following production plan, use a (a) Chase production strategy (b) Level production strategy to compute the monthly production, ending inventory / (backlog) and workforce levels. A worker...
Proof that If a group G contains an element a having exactly two conjugates, then G has a proper normal subgroup N (e).
If N is a simple normal subgroup of a group G and G/ N has a composition series, then G has a composition series.
It is July 30, 2015. The cheapest-to-deliver bond in a September 2015 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2015. Coupon payments...
What monopolies are you aware of? In your opinion, are monopolies good or bad for the economy, why?
What is a language-based learning disability.Discuss the relationship between pragmatic language skills and social difficulties of children with learning disabilities
On January 1, 2025, Atlantic Corporation purchased 40% of the common shares of Pacific Company for $185,000. During the year, Pacific earned net income of $91,000 and paid dividends of $22,750....
Are the missing invoices for the same or different customer accounts? If the same how can't his be an implication of fraud?
What doe IFRS 9 describe for hedge accounting for hedges of foreign currency assets & liabilities?
Cambridge Manufacturing is evaluating the introduction of a new product that would have a unit selling price of $100. The total annual fixed costs are estimated to be $200,000, and the unit variable...
Transform the while loop from the previous exercise into an equivalent for loop (make sure it produces the same output).
Rats with cancer are divided into two groups. One group receives 5 milligrams (mg) of a medication that is thought to fight cancer, and the other receives 10 mg. After 2 years, the spread of the...
Seventh-grade students are randomly divided into two groups. One group is taught math using traditional techniques;the other is taught math using a reform method. After 1 year, each group is given an...
A study in which balding men were compared with non-balding men at one point in time found that balding men were 70% more likely to have heart disease? Determine whether the study depicts an...
Light is incident into the gap between two plane parallel mirrors and just strikes the end of one mirror as shown in the diagram and them makes multiple reflections before leaving the gap. If d=5 cm,...
1. A hockey puck has a gravitational potential energy of 2.3 J when it is held by a referee at a height of 1.4 m above the rink surface. What is the mass of the puck? A: 2 2. A 200-g piece of iron at...
On an essentially frictionless, horizontal ice rink, a skater moving at 6.0 m/s encounters a rough patch that reduces her speed by 41% due to a friction force that is 29% of her weight. Part A Use...

Proof that Let X = { a i| i I| be a set. Then the free

Question:

Step by Step Answer:

To prove that the free abelian group on the set X denoted as FX is isomorphic to the group defined by the generators X and the relations aiajai1aj1 e ...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions