If : G H is a homomorphism, H is abelian and N is a subgroup of
Question:
If ∫: G → H is a homomorphism, H is abelian and N is a subgroup of G containing Ker ∫, then N is normal in G.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (6 reviews)
Let g G and n N We need to show that gng N for all n N S...View the full answer
Answered By
Morris Maina
I am a professional teaching in different Colleges and university to solved the Assignments and Project . I am Working more then 3 year Online Teaching in Zoom Meet etc. I will provide you the best answer of your Assignments and Project.
0.00
0 Reviews
10+ Question Solved
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
Students also viewed these Mathematics questions
-
Prove that x n - y n isdivisible by (x-y) for any x,y andany n
-
Show that N is a maximal ideal in a ring R if and only if R/N is a simple ring, that is, it is nontrivial and has no proper nontrivial ideals. (Compare with Theorem 15.18.) Data from Theorem 15.18 M...
-
If : G H is a homomorphism with kernel N and K < G, then prove that -1 ( (K)) = KN. Hence -1 ((K)) = K if and only if N < K.
-
The need to be liked and to stay on good terms with most other people is the need for? a. Affiliation b. Power c. None of the above d. Achievement
-
A Gallup survey indicated that 72% of 18- to 29-year-olds, if given a choice, would prefer to start their own business rather than work for someone else. A random sample of 600 18- to 29-year-olds is...
-
Show the structures of alkenes that give the following products on oxidative cleavage with KMnO4 in acidic solution: (b) (CH])2 + |(a) CHCH2CO2 co2 CH3CH2CH2CO2H (d) (c) (CH3)2C=0 CCH-CCH2CH2CHCH2CO2H
-
Which of the following control procedures would most likely assure that access to shipping, billing, inventory control, and accounting records is restricted to personnel authorized by management? a....
-
The adjusted trial balance for Amit Company is given in E4-16. Instructions Prepare the closing entries for the temporary accounts at August 31.
-
What are the general rules for deciding which method is used to account for an investment in the stock of another company? What are bonds? What are the characteristics of bonds? What factors affect...
-
1. Which process should VBB choose to produce?? 2. How much would VBP be willing to pay for the testing that is currently offered, for each batch?? 3. Would we be considered a perfect test, at twice...
-
Let G be an abelian group and let H,K be subgroups of G. Show that the join H V K is the set {ab| a H, b K}. Extend this result to any finite number of subgroups of G.
-
If : G 1 G 2 and g: H 1 H 2 are homomorphisms of groups, then there is a unique homomorphism h : G 1 * H 1 G 2 * H 2 such that h|G 1 = and h| H 1 = g.
-
A firm is considering launching a new product. Launching the product will require an investment of $10 million (including marketing expenses and the costs of new facilities). The launch is risky...
-
Holmes, Inc. expects net cash flow from operating activities to be $160,000, and the company plans purchases of equipment of $83,000 and repurchases of stock of $24,000. What is Holmess free cash...
-
How should you record a capital expenditure? a. Debit a liability b. Debit capital c. Debit an expense d. Debit an asset
-
Mountain Water Corp. issued common stock of $28,000 to pay off long-term notes payable of $28,000. In what section(s) would these transactions be recorded? a. Financing activities payment of note,...
-
What are the implications of divergency and complexity in the fast-food business?
-
Leather Shop earned net income of $57,000 after deducting depreciation of $5,000 and all other expenses. Current assets decreased by $4,000, and current liabilities increased by $8,000. How much was...
-
Look at the phase diagram for sulfur in Figure 11.12, bottom. What states of sulfur would you expect to see at each of the triple points? What solid phase would you expect to freeze out if you cooled...
-
Q:1 Take any product or service offered in Pakistan and apply all determinents of customer Perceived value ?
-
How does using a narrative record differ from using a checklist?
-
Explain how qualitative research differs from quantitative research.
-
Explain the archival method.
-
What is the problems with selecting a jury pool that reflects our racially diverse populations? What are two ways to improve jury selection to ensure that a criminal defendant has a jury that can be...
-
If a compliance officer discovered illegal activity by a company. An investigation has confirmed the activity, and legal counsel has advised the Boardof Directors that the information must be...
-
What is the difference between asking whether something is legal and whether something is ethical? Why is an engagement letter important and what should be included in an engagement letter? What are...
Study smarter with the SolutionInn App