Let F be the free group on the set X, and let Y X. If His

Question:

Let F be the free group on the set X, and let Y ⊂ X. If His the smallest normal subgroup of F containing Y, then F/ His a free group.

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 13, 2023 03:09 AM

See More Questions

The group G contains a subgroup P of order 7 such that the smallest normal subgroup of G containing P is G itself. ex = x and (gig)x gi(gzx).
If one attempted to dualize the notion of free module over a ring R (and called the object so defined "co-free") the definition would read: An R-module F is co-free on a set X if there exists a...
If (1) N G, then N = G; hence G is simple. [Use Exercise 18 to show P < N; apply Exercise 19.] Data from exercise 18 If (1) N 1 G, then 7 divides |N|. Data from exercise 19 The group G contains a...
For each of these utility functions, find the optimal consumption choices z and y for a consumer with budget w = 1, who faces prices pz = 0.05 and Py = 0.3. Are the goods substitutes or complements,...
According to the 2008 American Community Survey, 27% of residents of the United States 25 years old or older had earned at least a bachelors degree. You are performing a study and would like at least...
1. Would it be best for Victoria Oilfield Equipment to select a manager who is a local (citizen of Nigeria), a home country national (citizen of the United States), or a third-country national...
Find the mean and the standard deviation of the distribution of each of the following random variables (having binomial distributions): (a) The number of heads in 440 flips of a balanced coin. (b)...
Salvania Corporation is considering investing in Farnorth Corporation, but is unsure about what level of ownership should be undertaken. Salvania and Farnorth have the following reported incomes:...
Lamonda Corporation uses a job order cost system. On April 1, the accounts had balances as shown in the T- accounts below: The following transactions occurred during April: a. Purchased materials on...
Repeat problem 6, but close the position on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify the...
If : G His a homomorphism, a G, and(a) has finite order in H, then lal is infinite or I(a)I divides lal.
Break class into small groups of three to five students. Have students read the discussion question and discuss their answers within their groups. Students should be prepared to provide examples....
For each of the topics you selected in item 4-17, how might you use a more passive (observation) approach to support the communication methods you employ?
Consider this model in which national income Y depends on the previous periods income and the current and previous periods money supply M: where the parameters , 1 , 2 , and 3 are positive. a. If...
Should NASA expand the space shuttle program from four launches per year to five?
In a new highly automated factory, labor costs are expected to decrease at an annual rate of 5 percent; material costs will increase at an annual rate of 4 percent; overhead costs will increase at 8...
In 500 words or less, use cost-benefit analysis to explain some pattern of events or behavior you have observed in your own environment.
Go to the World Trade Organization's website http://stat.wto.org/StatisticalProgram/ WSDBStatProgram Home.aspx? Language=E, and click "selection." For Subject, add "Total merchandise trade to the...
Explain how this arrangement might have influenced New Zealands short-run Phillips curve. The Reserve Bank of New Zealand signed an agreement with the New Zealand government in which the Bank agreed...
Consider the advantages and disadvantages of extending property rights so that everyone would have the right to prevent people imposing any costs on them whatsoever (or charging them to do so).
What is the probability that a 30-year-old IDDM male patient will go blind over the next 10 years? Ophthalmology, Diabetes A study [12] of incidence rates of blindness among insulindependent...
After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time? Ophthalmology,...
What does cumulative incidence mean, in words, in the context of this problem? Ophthalmology, Diabetes A study [12] of incidence rates of blindness among insulindependent diabetics reported that the...
Gault Corporation had the following shares of stock outstanding on December 31, 2022: Common stock, $50 par value, 200,000 shares outstanding Preferred stock, 8%, $100 par value, cumulative, 20,000...
Golden Food Products produces special-formula pet food. The company carries no inventories. The master budget calls for the company to manufacture and sell 123,500 cases at a budgeted price of $60...
Rustafson Corporation is a diversified manufacturer of consumer goods. The company's activity- based costing system has the following seven activity cost pools: Estimated Overhead Cost Expected...

Let F be the free group on the set X, and let Y X. If His

Question:

Step by Step Answer:

To prove that FH is a free group we need to show that there exists a subset S of FH such that every element of FH can be uniquely expressed as a produ...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions