{a) A 4 is not the direct product of its Sylow subgroups, but A 4 does have
Question:
{a) A4 is not the direct product of its Sylow subgroups, but A4 does have the property: mn = 12 and (m,n) = 1 imply there is a subgroup of order m.
(b) S3 has subgroups of orders 1, 2, 3, and 6 but is not the direct product of its Sylow subgroups.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (5 reviews)
a To show that A4 is not the direct product of its Sylow subgroups note that A4 has two Sylow 3subgr...View the full answer
Answered By
Mary Boke
I have teached the student upto class 12th as well as my fellow mates.I have a good command in engineering,maths and science.I scored 90+ marks in 10th and 12th in maths.
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
-
For the matrix E below, find vectors b and c so that the system LS(E, b) is consistent and LS(E, c) is inconsistent. 4 1 1 6
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
S 3 is not the direct product of any family of its proper subgroups. The same is true of Z pn (p prime, n 1) and z.
-
To load and register a JDBC driver, two popular methods can be used: either using the Class.forName() method or creating a new instance of the Driver class.(True/False)
-
Access Samsungs website www.samsung.com/us/aboutsamsung/corporateprofile/history06.html and research the companys history. Also, review its 1938 to 1970 history at en.wikipedia.org/wiki/Samsung. 1....
-
Create an application, using the following names for the solution and project, respectively: Parking Solution and Parking Project. Save the application in the VB2015\ Chap11 folder. The application...
-
What are five common methods for distributing partnership earnings?
-
Al Quick, the president of a New York Stock Exchange-listed firm, is very short-term oriented and interested in the immediate consequences of his decisions. Assume a project that will provide an...
-
Kim acquired the following new assets during 2022: Date Asset Cost April 11 Furniture $140,000 July 28 Trucks 240,000 November 3 Computers 170,000 Kim does not elect immediate expensing under 179....
-
Alex Yeoman Painting Co. of Yellowknife uses a purchases journal (page 21) and a general journal (page 32) to record the following transactions. The GST rate is 5%. The paint store has decided to...
-
(a) Find a normal series of D 4 consisting of 4 subgroups. (b) Find all composition series of the group D 4 (c) Do part (b) for the group A 4 (d) Do part (b) for the group S 3 X Z 2 . (e) Find all...
-
If G = G o > G 1 > > G n is a subnormal series of a finite group G, then |G| = 'n-1 II|G/G+1||G|.
-
The subring E[F] generated by E and F is a vector space over Kin the obvious way. The tensor product E K F is also a K-vector space . E and F are linearly disjoint over K if and only if the K-linear...
-
CARDENES CORP. Okay... here are some simple facts: The company makes paper clips. Every clip is exactly the same. At the beginning there was no WIP and at the end there was no WIP. You made 10...
-
Write the function prototype called compute. The function should have three parameters: an int, a double, and a long. The int parameter should have a default argument of 5, and the long parameter...
-
you are required to describe the natwest group and it opreates in and the dividend policy it has followed over the last 8 years. please divide the period into two sub period before pandemic and after...
-
(Related to Checkpoint 5.6) (Solving for i) You lend a friend $10,000, for which your friend will repay you $27,027 at the end of 5 years. What interest rate are you charging your "friend"? The...
-
Describe how your department or service delivery would need to be adjusted. For example, would you downsize, bring in more interns ( remember the hidden cost ) , reduce hours, decrease professional...
-
Students in a business statistics course performed a completely randomized design to test the strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until the...
-
The Smiths buy a house. They borrow 80 percent of the purchase price from the local ABC Savings and Loan. Before they make their first payment, ABC transfers the right to receive mortgage payments to...
-
In the federal governments Current Population Survey, the response rate for 20- to 29 year olds is 85%; for individuals at least 70 years of age it is 99%. Why do you think this is?
-
During every election, pollsters conduct exit polls to help determine which candidate people voted for. During the 2004 presidential election, pollsters incorrectly predicted John Kerry the winner...
-
Name two biases that led to the Literary Digest making an incorrect prediction in the presidential election of 1936?
-
You need to find out the type of uncertainty (demand uncertainty and supply uncertainty), strategies adopted by Lululemon and the impact of accepting a particular strategy in dealing with demand...
-
Develop a journal entries to record the following transactions of an Internal Service Fund: Paid salaries of $10,000. Additional salaries accrued but not paid totaled $300. Purchased equipment...
-
3. (20 points) Show that the exponential distribution has the memoryless property. That is, show that for st 0, P(X s|X t) = P(X s t).
Study smarter with the SolutionInn App