Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. the question is: let g be a finite group, h, k be

The question is: Let G be a finite group, H, K be normal subgroups of G,...

50.1K

Verified Solution

Question

Advance Math

The question is: Let G be a finite group, H, K be normalsubgroups of G, and H?K is also a normal subgroup of G. UsingHomomorphism theorem ( or First Isomorphism theorem) prove thatG/(H?K) is isomorphism to a subgroup of(G/H)Ă—(G/K). And give a example of group G withnormal subgroups H and K such that G/(H?K) ? (G/H)Ă—(G/K), withexplanation.

I was trying to find some solutions for the isomorphism proofpart, but they all seems to have the condition with H?K = {e} . Ican ensure that there is no missing condition in my question. Asthere is another subquestion which I've already know the solution,is about given H?K = {e} and show G/(H?K) is isomorphism to(G/H)Ă—(G/K).

Answer & Explanation Solved by verified expert
3.6 Ratings (657 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Bond Discount, Entries for Bonds Payable Transactions On July 1, Year 1, Danzer Industries Inc. issued...

Accounting
Q

For these binomial settings, give the parameters n and p. a) Orchid flowers can be “left-handed”...

Statistics
Q

You are assigned the task of determining the bacterial density of newly-grown culture. You decide that...

Biology
Q

Rogot Instruments makes fine violins and cellos. It has ?$1.7 million in debt? outstanding, equity valued...

Finance
Q

c 384 Hz d 500 Hz 29 A particle executes SHM with an amplitude of...

Physics
Q

Watch the video that describes expressing cos A B as a function of a single...

Geometry
Q

What is the measure of Angle B A C m B 67 53 B

Basic Math
Q

10. The deadweight loss of a tax is A) the reduction in...

Accounting
Q

Investor Inc. owns 40 percent of Alimand Corporation. During the calendar year 20X5, Alimand had...

Accounting
Q

Determine the expenses for August based on the following data, (Click on the icon to...

Accounting
Q

What does the acid-test (quick) ratio measure? a) A company's ability to pay...

Accounting
Q

A company borrowed $30,000 by signing a 120-day promissory note at 8%. The total interest...

Accounting