Every finitely generated abelian group G (e) in which every element (except e ) has order

Question:

Every finitely generated abelian group G ≠ (e) in which every element (except e) has order p (p prime) is isomorphic to Z_p ⊕Z_p·· •⊕Z_P (n summands) for some n ≥ 1.

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 03:08 AM

See More Questions

Deal with the concept of the torsion subgroup just defined. An abelian group is torsion free if e is the only element of finite order. Use Theorem 11.12 to show that every finitely generated abelian...
Describe all subgroups of order 4 of Z 4 x Z 4 , and in each case classify the factor group of Z 4 x Z 4 modulo the subgroup by Theorem 11.12. That is, describe the subgroup and say that the factor...
Which type of philosophical reasoning begins with one example and varies it to see how dramatic the change is, which uncovers its most crucial characteristics?
The following frequency distribution represents the heights (in inches) of 80 randomly selected 5-year-old females. (a) Use MINITAB or some other statistical software to construct a relative...
Can the reliability and validity of qualitative research be determined? If yes, what are some methods to do so?
4. What does Net Settlement mean?
One Travel provides travel services on the Internet. 2011 was an important year for One Travel as it reported positive operating income after 3 years of operating losses. In the first quarter of...
For each the following accounts, indicate (a) if the account is an asset, liability, or owners equity account; and (b) whether the account would have a normal debit or credit balance. Account (a) (b)...
Income Statement, Statement of Owner's Equity, and Balance Sheet Paulson's Pet Store completed the Adjusted Trial Balance for the year ended December 31, 20--. Owner's equity as of January 1, 20--,...
Prove that if all the sets in the family {A i Ii I } are nonempty, then each of the projections is surjective. k: II A Ak
Let H,K be subgroups of a group G. Then HK is a subgroup of G if and only if HK= KH.
A developer acquired a parcel of unimproved real property that she would like to develop. Although the land is currently zoned for commercial use, the developer would prefer not to begin development...
Haley Romeros had just been appointed vice president of the Rocky Mountain Region of the Bank Services Corporation (BSC). The company provides check processing services for small banks. The banks...
Draw a simple but complete hydraulic circuit diagram to drive two actuators, one of which must be connected to a pressure reducing valve to control its pressure because of the delicacy of the task...
1. What specific skills would a person have to be a successful director for a parks and recreation position? 2. What experience would a person have working with an elected board for parks and...
Required labor time per unit ( hours ) Maximum demand ( units ) Contribution margin per unit Product M 2 6 , 5 0 0 $ 5 . 0 0 Product N 3 8 , 0 0 0 $ 5 . 7 0 If Bush uses the most effective approach...
ansewr pls Repeat Exercise 5.8.1 using (a) one rectangle; (b) four rectangles. Data From Exercise 5.8.1 A square plate size $100 \mathrm{~cm} \times 100 \mathrm{~cm}$ is subjected to an isothermal...
Suppose that the Fed raises its interest rate target to prevent the economy from overheating. Illustrate graphically, using a diagram similar to Figure 7, but this time include the feedback effects...
Suppose you won a financial literacy competition and are given FJS10000 to invest, with the condition that investment can be done either in, i) Invest in Unit trust of Fiji or Invest in Fijian...
Compute the PV under these altered assumptions. How does the true PV using a screening criterion of SCN 100 g/mL for identifying smokers compare with the PV based on self-reports obtained in Problem...
If the manual measurements are regarded as the true measure of reactivity, then what is the sensitivity of automated DBP measurements? Hypertension Laboratory measures of cardiovascular reactivity...
What is the specificity of automated DBP measurements? Hypertension Laboratory measures of cardiovascular reactivity are receiving increasing attention. Much of the expanded interest is based on the...
Suppose the S&P 500 currently has a level of 960. One contract of S&P 500 index futures has a size of $250 S&P 500 index. You wish to hedge an $800,000-portfolio that has a beta of 1.2. (A)In order...
Exhibit 4.1 The balance sheet and income statement shown below are for Koski Inc. Note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during...
Haley is 57 years of age. She is planning for future long-term care needs. She knows that yearly nursing home costs in her area are currently $69,000, with prices increased by 5 percent annually....

Every finitely generated abelian group G (e) in which every element (except e ) has order

Question:

Step by Step Answer:

This statement is a special case of the fundamental theorem of finitely generated abelian groups Let ...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions