Question

For which integers n such that 3<= n <=11 is there only one group of order n (up to isomorphism)?

(A) For no such integers n

(B) For 3, 5, 7, and 11 only

(C) For 3, 5, 7,9, and 11 only

(D) For 4, 6, 8, and 10 only

(E) For all such integers n

Answer #1

The correct option is (B)

Because if n is a prime number P, then any group is isomorphic to Zp. Since 3,5,7,11 are prime numbers then upto isomorphism they are isomorphic to only Z3, Z5, Z7, Z11.

But there are 2 groups of order 4 upto isomorphism, namely Z4, K4. (klien's 4 group).

There are 2 groups of order 6, namely S3 and Z6.

There are 3 groups of order 8, namely, Z8, D4, Z4xZ2.

There are 2 groups of order 9, namely, Z9, Z3xZ3.

SO option B is correct option (justied)

Characterize those integers n such that any Abelian group of
order n belongs to one of exactly four isomorphism classes.

Characterize those integers n such that any abelian group of
order n belongs to one of exactly two isomorphism classes.

n x n matrix A, where n >= 3. Select 3 statements from the
invertible matrix theorem below and show that all 3 statements are
true or false. Make sure to clearly explain and justify your
work.
A=
-1 , 7, 9
7 , 7, 10
-3, -6, -4
The equation A has only the trivial solution.
5. The columns of A form a linearly independent set.
6. The linear transformation x → Ax is one-to-one.
7. The equation Ax...

ANSWER IN C++ ONLY
A string of characters including only alphabets (lowercase
letters) is provided as an input.
The first task is to compute the frequency of each character
appearing in the string. In the output, the characters have to be
arranged in the same order as they appear in the input string.
Then characters have to be rearranged, such that all the
characters having a specific frequency, say xx, come together.
Let the frequency of a character, lying in...

Fatty acids that are unsaturated have:
Select one:
a. an amino group
b. a double bond
c. an excess of protons
d. a carboxyl group
The following structure is solid at room temp with the maximum
amount of hydrogens attached and has no double bonds. What is
it?
Select one:
a. An unsaturated fat
b. A protein
c. A solute
d. A saturated fat
Although there are a limited number of amino acids, many
different types of proteins exist because...

Six integers are given in this order: 8, 4, 3, 5, 9, and 6. Do
each of the following. SHOW YOUR WORK step by step.
1. Create an AVL tree by inserting the integers in the given
order.

1) You must implement a recursive Quicksort algorithm that will
read integers from the attached MyList.txt file. Your algorithm
must sort the list(integers)in ascending order.
2)You must implement a recursive Mergesort algorithm that will
read integers from the attached MyList.txt file. Your algorithm
must sort the list(integers)in ascending order.
My List txt Values
7
3
4
1
4
4
9
9
4
8
4
5
3
9
2
3
7
0
6
4
4
5
0
1
9
2
1...

Observation Number
Observation
1 -11
2 -11
3 -11
4 -15
5 -17
6 -17
7 -20
8 -24
9 -25
10- 26
11 -28
12 -28
13 -29
14 -31
Calculate:-
A. MODE
B. 90TH PERCENTILE
C. STANDARD DEVIATION (ROUND THE ANSWER TO ONE DECIMAL
PLACE)
D. MEDIAN

PYTHON
Ask the user for a value N (0 ≤ N < 10)
Create a 2-D list in an N X N structure with integers
1-(N*N)
Print the list created
Reverse the list such that (1) each list in the 2D list is
reversed and (2) the order of each list in the outer list is
reversed (see example)
Print the reversed list
Example Execution
What size 2D list would you like to create?
N> 3
The original list is:...

5. Prove that the mapping given by f(x) =x^3+1 is a function
over the integers.
6. Prove that f(x) =x^3+is 1-1 over the integers
7. Prove that f(x) =x^3+1 is not onto over the
integers
8 Prove that 1·2+2·3+3·4+···+n(n+1)
=(n(n+1)(n+2))/3.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 31 minutes ago

asked 41 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago