If N is a nontrivial normal subgroup of a nilpotent group G, then N C(G)

Question:

If N is a nontrivial normal subgroup of a nilpotent group G, then N ∩ C(G) ≠ (e).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

See More Books

Question Posted: Apr 15, 2023 03:51 AM

See More Questions

(a) Show that the analogue of Theorem 7.11 is false for nilpotent groups [Consider S 3 ]. (b) If H < C( G) and G/H is nilpotent, then G is nilpotent. Theorem 7.11 (i) Every subgroup and every...
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...
Let G be a group, and let P(G) be the set of all subsets of G. For any A, B P(G), let us define the product subset AB = {ab | a A, b B}. a. Show that this multiplication of subsets is associative...
Jarvis Company produces a product that has a selling price of $20.00 and a variable cost of $15.00 per unit. The company's fixed costs are $50,000. What is the break-even point measured in sales...
Why do economists believe government failure is inevitable?
For your final project, you'll need access to the case file from Harvar and the link for purchase is https://hbsp.harvard.edu/import/1046501Links to an external site. (Links to an external site.)(...
What is a Wohler curve?
1. If you were Skip Grenoble, which alternative would you advice Jim Beierlein to implement? What criteria would you use to arrive at your decision? 2. At what level of demand (in pounds) per year...
The following information relate to the business of Katwishi as at 31-12-16 K'000 Purchases Sales Returns inwards Returns outwards Debtors 64,700 125,600 6,340 1,900 11,250 Creditors 7,900...
A small rock with mass 0.10 kg is released from rest at point. A, which is at the top edge of a large, hemispherical bowl with radius R=0.60 m (the figure (Figure 1)). Assume that the size of the...
Proof that A nonzero free abelian group has a subgroup of index n for every positive integer n.
Use the Krull-Schmidt Theorem to prove Theorems 2.2 and 2.6 (iii) for finite abelian groups. Data From Theorem 2.2 Every finitely generated abe/ian group G is (isomorphic to) a finite direct sum of...
What possible scenario is described by the energy diagram in Figure P9.15? Data from Figure P9.15 AK AU , W
You have been recently promoted to the position of Total Compensation manager for your firm, a retail company specializing in sustainable clothing. There has been a trend of poor performance and high...
Offer your description or definition of excellent service at the time of check-in for: at a motel on a highway? at a full service Ritz-Carlton Hotel?
Name and explain the three core worker rights under Ontario's Occupational Health Safety Act. Explain the due diligence defense. What steps can employers take to establish this defense?
John is looking for a new car. He has a down payment of $1,000.00 and wants to pay $250.00 per month for 5 years. The best deal he found for an amortized loan is his local bank, at a rate of 2.95%....
What is an assessment center (AC)? What kind of exercises or activities can be included in an AC? Explain.
A firm received a bill from its accountant for $3310, representing a combined total of 41 billable hours for both the Certified General Accountant (CGA) and her accounting technician, for conducting...
From 1970 to 1990, Sri Lanka's population grew by approximately 2.2 million persons every five years. The population in 1970 was 12.2 million people.What is the best formula for P, Sri Lanka's...
What test can be performed to compare the variances of the two groups? Orthopedics A study was performed among patients with piriformissyndrome (PS), a pelvic condition that involves malfunction of...
Obtain a 95% CI for the mean difference in diet record vitamin C intake between the two groups? Nutrition The EPIC-Norfolk study, a study of diet and cancer in Great Britain, was performed to assess...
Implement the procedure in Problem 9.2, and report a p-value? Suppose patients are graded on the degree of change in periodontal status on a 7-point scale, with +3 indicating the greatest...
Crane Financial Planners Adjusted Trial Balance December 31, 2020 Debit Credit Cash Accounts Receivable Supplies Equipment $6,174 2,898 2,268 17.640 Accumulated Depreciation-Equipment $3.780 Accounts...
A comapny has issued a $ 1 6 2 , 0 0 0 , 3 ?year, zero interest bond dated January 1 , 2 0 2 3 . ?The market interest rate for similar bonds was 1 1 % . ?Assume the company used the effective...
a) The butadiene molecule CH-CH-CH-CH; has alternating double and single bonds. Such molecules are called conjugated and as an approximation the pi electrons can be considered as free. The length of...

If N is a nontrivial normal subgroup of a nilpotent group G, then N C(G)

Question:

Step by Step Answer:

ANSWER We will prove the statement by contradiction Assume that N CG e where e is the identity eleme...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions