Show that if a group G with identity e has finite order n, then a n =

Question:

Show that if a group G with identity e has finite order n, then aⁿ = e for all a ∈ G.

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

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

See More Books

Question Posted: Dec 30, 2022 03:13 AM

See More Questions

Show that every group G with identity e and such that x * x = e for all x G is abelian.
Show that if a one-way analysis of variance is per-formed on the ranks of the observations instead of the observations themselves, it becomes equivalent to a test based on the H statistic.
Show that if a 0 and b 0, then there exist numbers a and such that aex + be-x equals either or sinh(x + ) or cosh(x + ), In other words, almost every function of the form f(x) = aex + be-x is a...
Write the boldfaced numbers in each problem in scientific notation. The largest of the 50 United States is Alaska, with land area of about 365,482,000 acres, while the smallest is Rhode Island, with...
With whom does the auditor interact most shareholders, the Board of Directors, or management?
Explain how you could use techniques such as focus groups, group support systems, RISK, and PERT to help at various stages of P-MOPS.
15. What 8-quarter dollar annuity is equivalent to an 8-quarter annuity of =C1?
Obtain an estimate of the integral from Prob. 22.1, but using two-, three-, and four point Gauss-Legendre formulas. Compute t for each case on the basis of the analytical solution.
Part A Santana Rey of Business Solutions is evaluating her inventory to determine whether it must be adjusted based on lower of cost or market rules, Business Solutions has three different types of...
a. From a process standpoint, evaluate how well this investigation began to unfold. b. Should Barbara have done anything differently? c. What changes, if any, would you recommend be made to the...
Deal with the concept of the torsion subgroup just defined. Find the torsion subgroup of the multiplicative group R * of nonzero real numbers.
The Study of Regular Division of the Plane with Reptiles in Fig. 12.10. Figure 12.10 This exercise is concerned with art works of M. C. Escher. Neglect the shading in the figures and assume the...
The trial balance columns of the worksheet for Dixon Company at June 30, 2017, are as follows. Other data: 1. A physical count reveals $500 of supplies on hand. 2. $100 of the unearned revenue is...
Q3: In the section illustrated in Figure (1) the surface 1-4-7 is insulated. The convection heat transfer coefficient at surface 1-2-3 is 28W / (m ^ 2) ."C. The thermal conductivity of the solid...
Which of the following best demonstrates the Six Cs of Communication, "you" approach, and positive emphasis? Question 1 4 options: It will be February 1 0 before you will receive your materials. It...
please answer all the questionss.,.within 30 minutes. make sure the explanation and reasons are explained in very detailed manner as in why the chosen option is right and why other options are wrong....
1) A net force of 20 N is applied to the right on an object. If the acceleration of the object is 2.5 m/sec, a) What is the mass of the object? (8 kg) b) What is the weight of the object? (78.4 N) c)...
BO Corp. has a $2,500 capital budget, and has access to the following 5 independent projects. In all these 5 projects, cash outflows occur only in year O. Calculate the total NPV of the project(s)...
You would like to own a common stock that has a record date of Friday, September 8, 2017. What is the last date that you can purchase the stock and still receive the dividend?
To help you become familiar with the accounting standards, this case is designed to take you to the FASBs Web site and have you access various publications. Access the FASBs Web site at...
What test can be performed to compare the mean change in the two groups at 18 months? Mental Health A study was performed looking at the effect of physical activity on cognitive function among adults...
Implement the test in Problem 8.79, and report a two-sided p-value? Mental Health A study was performed looking at the effect of physical activity on cognitive function among adults at high risk for...
1. Compare degree of pain while on Motrin with degree of pain on placebo during maximal activity? 2. Answer Problem 8.81 for degree of pain 12 hours following maximum activity? 3. Answer Problem 8.81...
The following schedule reconciles Cele Co.'s pretax GAAP income Pretax GAAP income Nondeductible expense for fines Tax deductible depreciation in excess of GAAP depreciation expens Taxable rental...
How to solve general ledger cash balance chapter 9 assignment 5
On 31 July 2018, Sipho bought 1 000 ordinary shares in ABC Ltd at a cost of R2 750. On 31 December 2018 the company made a 1 for 10 bonus issue. On 31 March 2019, Sipho sold 300 shares for R800. What...

Show that if a group G with identity e has finite order n, then a n =

Question:

Step by Step Answer:

Let a G Then a has order ...View the full answer

A First Course In Abstract Algebra

Students also viewed these Mathematics questions