Let G be an (additive) abelian group with subgroups H and K. Show that G H
Question:
Let G be an (additive) abelian group with subgroups H and K. Show that G ≅ H ⊕ K if and only if there are homomorphisms
such that π1L1 = 1H, π2L2 = 1K, π1L2 = 0 and π2L1 = 0, where 0 is the map sending every element onto the zero (identity) element, and L1π1(x) + L2π2(x) = x for all x ϵ G.
Transcribed Image Text:
H ܙ 41 G K 42
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (6 reviews)
Suppose that G H K Then there exist homomorphisms H K G and G H K such that 1HK and 1G Let 1 H K H a...View the full answer
Answered By
Anik Kumar Bosu
I am expert in Maths, Physics, Chemistry and Biology. I also teach student from 3 years. Students becomes satisfied by my teaching. So, do not worry.
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
-
let g be an abelian group with identity e and hLet L(y) an y(n)(x) an 1 y(n 1)(x) a1 y(x) a0 y(x) where a0, a1, , an are fixed constants Consider the nth order linear differential equation L(y) 6e5x...
-
Let G be a group with subgroups H and K. If |G| = 660, |K| = 66, and K H G, what are the possible values for |H|?
-
Find out the interference pattern measured at the output port of the Michelson interferometer when a single-frequency laser beam is applied.
-
1. Prepare program using threads in java that can print 10 times the numbers 1,2,3,4,5 in a series. 2. Prepare program using threads and a semaphore in java that can print the numbers 1,2,3,4,5 in a...
-
According to a Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (ction and nonction) within the past year. You conduct a random sample of 250 Americans...
-
The Blackstar Fund has assets with a market value of $12.6 million and liabilities of $800,000. What is the net asset value (NAV) if there are 200,000 shares outstanding?
-
A [0/90/0] laminated beam of length \(L\) is simply supported at both ends and is loaded by a single concentrated load \(P\) at midspan. Find the equation for the maximum flexural deflection of the...
-
In August 2015, the last month of its scal year, Goldwaithe Township issued $88,000 worth of tickets for parking and trafc violations. Of these, the township collected $45,000. It expects to collect...
-
1: Explain what elasticity of demand means. Support your explanation with a suitable example. 2: Describe the relationship between elasticity of demand and revenue when the prices are changed. 3:...
-
Wayland Custom Woodworking is a firm that manufactures custom cabinets and woodwork for business and residential customers. Students will have the opportunity to establish payroll records and to...
-
(a) Prove that S n is generated by then - 1 transpositions (12), (13), (14), ... , (In). (b) Prove that S n is generated by the n - 1 transpositions (12), (23), (34), ... , (n - 1n).
-
A group G is abelian if and only if the map G G given by x | x -1 is an automorphism.
-
In what ways is the implementation of an ERP system simpler and less risky for an SME than for a large multinational corporation?
-
Laguna Manufacturing is considering replacing a piece of equipment with a newer, more efficient model. The old equipment was purchased several years ago for $112,500 and has annual operating costs of...
-
Patient has outstanding balance $25 for service 12/31/23 only. please see message below. Hello, I received a letter showing an outstanding balance for two of Nilou's visits; 1. 12/31/23 Isabel...
-
P2a. Various financial data for the past two years follow. Calculate the productivity ratios and enter the % change (round to one decimal place) from last year to this year. Output: Inputs: Volume (#...
-
Please use this assignment to submit the various Research Essay First Draft revisions that we discussed in class. Choose FOUR sections that need improvement (the Introduction, a Body Paragraph, a...
-
What are the 3 questions (in order of sequence) to analyze business transactions? Explain.
-
In the Excel file Gasoline Prices, determine if there is evidence to conclude that the variance of weekly prices during 2009 is less than 10%.
-
The first national bank pays a 4% interest rate compound continuously. The effective annual rate paid by the bank is __________. a. 4.16% b. 4.20% c. 4.08% d. 4.12%
-
What is the expected value and variance for a Poisson distribution with parameter = 4.0? Suppose we want to check the accuracy of self-reported diagnoses of angina by getting further medical records...
-
If 500 newborns are screened at the inner-city hospital, then what is the exact binomial probability of exactly 5 HIV-positive test results? Infectious Disease Newborns were screened for human...
-
If 500 newborns are screened at the inner-city hospital, then what is the exact binomial probability of at least 5 HIV-positive test results? Infectious Disease Newborns were screened for human...
-
The following unadjusted trial balance is for Ace Construction Company at its June 3 0 current fiscal year - end. The credit balance of the V . Ace, Capital account was $ 5 3 , 0 0 0 on June 3 0 of...
-
The Following Information pertains to teh CIty of Williamson for 2 0 2 0 , its first year of legal existence. For convenience, assume that all transactions are for the general fund, which has three...
-
Golf Academy, Incorporated, provides private golf lessons. Its unadjusted trial balance at December 3 1 , 2 0 2 1 , follows, along with information about selected accounts. Account Names Debit Credit...
Study smarter with the SolutionInn App