Every subgroup and every quotient group of a nilpotent group is nilpotent.
Question:
Every subgroup and every quotient group of a nilpotent group is nilpotent.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (6 reviews)
Let G be a nilpotent group and let H be a subgroup of G We want to show that H is nilpotent Since G ...View the full answer
Answered By
Prince Kumar
I have teaches last 5 year in difference Colleges and universities. I'm principal in secondary school last 2 year.
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
-
A square matrix A is called nilpotent if Ak = O for some k 1. (a) Prove that the only eigenvalue of a nilpotent matrix is 0. (The converse is also true; see Exercise 8.6.18.) (b) Find examples where...
-
Show that for a finite group, every refinement of a subnormal series with abelian quotients also has abelian quotients, thus completing the proof of Lemma 56.3. Data from Lemma 56.3 Let F be a field...
-
Mark each of the following true or false. ___ a. Every subgroup of every group has left cosets. ___ b. The number of left cosets of a subgroup of a finite group divides the order of the group. ___ c....
-
Assuming @Weather is a valid repeatable annotation that takes a String, with its associated containing type annotation @Forecast, which of the following can be applied to a type declaration? (Choose...
-
Refer to the statements for Google in Appendix A. For the year ended December 31, 2013, what is its debt-to-equity ratio? What does this ratio tell us?
-
A fractionation column operating at 101 kPa is to separate 30 kgh of a solution of benzene and toluene containing 0.6 mass-fraction toluene into an overhead product containing 0.97 mass-fraction...
-
Describe the successes and failures of attempts to eliminate poverty between the end of World War II and the fall of the Soviet Union in 1991.
-
The Freema Company at December 31 has cash $20,000, non-cash assets $100,000, liabilities $55,000, and the following capital balances: Dalek $45,000 and Briggs $20,000. The firm is liquidated, and...
-
The following data relate to two investment projects, only one of which may be selected: Initial capital expenditure Net profit per year: Year 1 Year 2 Year 3 Project A Project B R R 1 400 000 1 400...
-
Jacqueline Ponce de Leon, a descendent of Juan Ponce de Leon, made a cash contribution of $1,500,000 to the City of Fountains to create and maintain a large fountain in front of City Hall in honor of...
-
Proof that An abelian group has a composition series if and only if it is finite.
-
(a) Show that there is a nonabelian subgroup T of S 3 X Z 4 of order 12 generated by elements a,b such that |a| = 6, a 3 = b 2 , ba = a -1 b. (b) Any group of order 12 with generators a,b such that...
-
For a firm considering expansion of its existing line of business, why is the WACC, rather than the cost of equity, the preferred discount rate if the firm has both debt and equity in its capital...
-
Explain the essential distinctions among the stages-of-growth theory of development, the structural-change models of Lewis and Chenery, and the theory of international dependence in both its...
-
Is the neoclassical, free-market theory necessarily incompatible with dependence theory? How might these two approaches work together?
-
Distinguish between size and functional distributions of income in a nation. Which do you conclude is the more appropriate concept? Explain your answer.
-
Social and institutional innovations are as important for economic growth as technological and scientific inventions and innovations. What is meant by this statement? Explain your answer.
-
It is sometimes asserted that small peasant farmers are backward and ignorant because they seem to resist agricultural innovations that could raise farm yields substantially. Does this resistance...
-
Write the balanced chemical equation for the reaction of each acid and base pair. a. HCl + C5H5N b. H2C2O4 + NH3 c. HNO2 + C7H9N
-
In a certain school district, 3% of the faculty use none of their sick days in a school year. Find the probability that 5 faculty members selected at random used no sick days in a given year.
-
What is the expected number of intermediate cells by age 45? The probability that an intermediate cell will mutate to become a malignant cell is 5 107 per year. Cancer The two-stage model of...
-
Suppose a woman has 300 intermediate cells by age 45. What is the probability that she develops breast cancer by age 46? By age 50? Cancer The two-stage model of carcinogenesis is based on the...
-
If we assume the average number of teeth lost in the 59 group is 7 teeth and the average number of teeth lost in the 10+ group is 12 teeth, what is the best estimate of the average number of teeth...
-
Calculate final RTO if initial RTO is 6s; Seg 1 sent at 0s, Seg 2 sent at 2s, ACKs for Seg 1 and Seg 2 are received at 5s, Seg3 sent at 8s, Seg 4 sent at 9s, ACKs for Seg3 & Seg4 lost, Seg3 and Seg4...
-
Problem 1: The sketch below is a side view of a water well's bucket, light rope and cylindrical windlass. The windlass handle is removed to allow the bucket to descend from rest at the top of the...
-
As new technologies are developed, the nature of eLearning is in a constant state of change and evolution. From the days of correspondence courses completed with paper and pens or typewriters to...
Study smarter with the SolutionInn App