Proof that If a group G contains a subgroup ( G) of finite index, it contains a
Question:
Proof that If a group G contains a subgroup (≠ G) of finite index, it contains a normal subgroup (≅G) of finite index.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 70% (10 reviews)
ANSWER This statement is true Heres a proof Let H be a subgroup of finite index in G ie GH is finite ...View the full answer
Answered By
User l_917591
As a Business Management graduate from Moi University, I had the opportunity to work as a tutor for undergraduate students in the same field. This experience allowed me to apply the theoretical knowledge I had gained in a practical setting, while also honing my teaching and communication skills.
As a tutor, I was responsible for conducting tutorial sessions, grading assignments and exams, and providing feedback and support to my students. I also assisted with the preparation of course materials and collaborated with other tutors and professors to ensure consistency in teaching and assessment.
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
-
Mark each of the following true or false. ___ a. Any two Sylow p-subgroups of a finite group are conjugate. ___ b. Theorem 36.11 shows that a group of order 15 has only one Sylow 5-subgroup. ___ c....
-
Proof that A nontrivial finite solvable group G contains a normal abelian subgroup H (e). If G is not solvable then G contains a normal subgroup H such that H' = H.
-
Completing a detail of the proof of Theorem 12.5, let G be a finite group of plane isometries. Show that the rotations in G, together with the identity isometry, form a subgroup H of G, and that...
-
Write a well-developed paragraph that compares/contrasts a character from Good Country People with a character from Seventeen Syllables.
-
What acts are regarded as the most significant pieces of prolabor legislation?
-
(a) Show that the radiation reaction force in the Lorentz-Dirac equation of Problem 16.7 can be expressed alternatively as (b) The relativistic generalization of A6.10) can be obtained by replacing...
-
You are conducting an experiment on the effectiveness of a reading intervention with young children and want to report the descriptive results to your colleagues. Some of the children received the...
-
Employee earnings records for Slaymaker Company reveal the following gross earnings for four employees through the pay period of December 15. J. Seligman .......$ 93,500 R. Eby...
-
San Diego Corp has 2,318,809 million shares of common stock outstanding witha par value of $1.00 per share. The current marketprice per share is $ 75. San Diego Corp hasoutstanding debt with a par...
-
Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residences in the Blacksburg area. The...
-
Every group G of order p 2 (p prime) is abelian.
-
(a) What are the elementary divisors of the group Z 2 Z 9 Z 35 ; what are its invariant factors? Do the same for Z 26 Z 42 Z 49 Z 200 Z 1000. (b) Determine up to isomorphism all abelian groups of...
-
In their 2017 financial statements, five international fashion retailers that is, Burberry, Esprit, French Connection, Inditex, and Next explicitly discussed their key accounting policies. The...
-
ABC Ltd has 10 million shares priced at 50 each. It plans to purchase 2,000,000 shares at the market price from its existing cash reserves. What will be the market capitalization and share price...
-
An empty hot tub has a mass of 320 kg. When filled, the tub holds 600 gallons of water ( = 62.4 lbm/ft3). The local acceleration due to gravity is 32 ft/s2. Determine the total weight of the hot tub...
-
ABC Ltd has 5 million shares priced at 50. It has excess cash of 50 million, which it decides to pay out as a one-time cash dividend. a. What is the ex-dividend price of a share? b. If the board...
-
ABC Ltd has a net profit of 400 million. The number of shares is 50 million. Given the nature of its business, the discount rate is 10 per cent. The company invests 30 per cent of its net profit on...
-
Established two and a half decades back, XYZ Ltd is engaged in Information Technology (IT) for mass consumption. Those were the early days for the IT sector in India, and the company had to battle...
-
If 5.55 1022 atoms of He occupy a volume of 2.06 L at 0(C at 1.00 atm pressure, what volume do 2.08 1023 atoms of He occupy under the same conditions?
-
-x/2 x/4 If A = -x/2 and A-1 =6 then x equals
-
Refer to Data Set FEV.DAT at www.cengagebrain.com . Assess whether there are any outliers in FEV for the following groups: 5- to 9-year-old boys, 5- to 9-year-old girls, 10- to 14-year-old boys, 10-...
-
What is the standard error of ln(ERG amplitude) among patients with dominant RP? How does it differ from the standard deviation in the table? Ophthalmology A study compared mean electroretinogram...
-
What test can be used to compare the variance of ln (ERG amplitude) between patients with dominant vs. recessive RP? Ophthalmology A study compared mean electroretinogram (ERG) amplitude of patients...
-
Write a pseudo code and draw flowchart to print all multiples of 5 between 1 and 1 0 0 ( including both 1 and 1 0 0 ) .
-
Explain the steps in a discrimination complaint to the EEOC.
-
Describe documents that are used in advancing litigation through the court system and explain their purpose and the sort of information that should be contained within them?
Study smarter with the SolutionInn App