an example of an abelian group which is not cyclic

Answers

Answer 1

G=Z6×Z2G=Z6×Z2 will do (where ZnZn denotes the cyclic group of order nn). As a direct product of cyclic (so abelian) groups, GG is again abelian. Given any element (x,y)∈G(x,y)∈G, the order of (x,y)(x,y) will be the least common multiple of the orders of x,y.x,y.  

The order of xx must divide 66 and the order of yy must divide 2,2, so the order of (x,y)(x,y) is at most lcm(6,2)=6.lcm⁡(6,2)=6. But |G|=|Z6|⋅|Z2|=6⋅2=12.|G|=|Z6|⋅|Z2|=6⋅2=12. Since no element of GG has order 12,12, then GG is not cyclic.


Related Questions

Mako runs 10 miles in 2 hours. If he continues at this rate, how many miles
will he run in 5 hours?
A. 50 miles
B. 10 miles
O C. 25 miles
O D. 30 miles

Answers

Answer:

Answer: 25 miles

Step-by-step explanation:

Explanation: He will run 5 hours= 5x5=25

Answer:

25 miles

Step-by-step explanation:

I'll create a set of proportions to figure out the answer (represented by x):

2:10 = 5:x

It looks like our proportion on the left, 2:10, can be simplified by dividing both sides by 2 to get 1:5.

1:5 = 5:x

You can multiply 1 by 5 to get 5, so we should be able to multiply 5 by 5 to get the value of x. 5 times 5 is 25, so the answer to the question is 25 miles.

If you have questions or need clarification on anything, let me know!

Today eight friends went for lunch there total bill was $34.56, including tax. One of them ordered always soda and needed to pay only $1.94. The other seven friends or the same daily special. How much did each of the other friends need to pay?

Answers

Answer:4,66

Step-by-step explanation: first , we subtracted 1 people . 34,56 - 1,94 = 32,62 . then we divided for seven people . we have : 32,62 : 7 = 4,66 each person

Anyone know thisss

its math

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The Correct choice is :

[tex]y - 2 = - 3(x - 2)[/tex]

12x – 9y = 135. Fully simplify your answer.

Answers

Answer:

[tex]x=\frac{3\left(y+15\right)}{4}[/tex]

Step-by-step explanation:

Answer:

I belive the answer is 15! Brainest?

Step-by-step explanation:

If
f(x) = 6x2 − x3,
find f '(1) and use it to find an equation of the tangent line to the curve
y = 6x2 − x3
at the point (1, 5).

Answers

Evaluate the derivative of f(x) at x = 1. I'll use the limit definition:

[tex]\displaystyle \lim_{x\to1} \frac{f(x)-f(1)}{x-1} = \lim_{x\to1} \frac{6x^2-x^3-5}{x-1} = \lim_{x\to1}(-x^2+5x+5) = 9[/tex]

Then using the point-slope formula, the equation of the tangent line to f(x) at the point (1, 5) is

y - 5 = 9 (x - 1)

y = 9x - 4

The equation of "tangent-line" to the curve "y = 6x² - x³" at the point (1, 5) is : y = 9x - 4.

To find the derivative of the function f(x) = 6x² - x³, we differentiate each term with respect to x:

f(x) = 6x² - x³,

f'(x) = d/dx (6x²) - d/dx (x³),

f'(x) = 12x - 3x²,

Now, we need to find f'(1), which means evaluating derivative at x = 1;

f'(1) = 12(1) - 3(1)²,

f'(1) = 12 - 3,

f'(1) = 9,

The slope of tangent-line at point (1, 5) is given by f'(1), which is 9;

Using the point-slope form of equation of line (y - y₁ = m(x - x₁)), where m = slope and (x₁, y₁) is the given point (1, 5);

⇒ y - 5 = 9(x - 1),

Simplify the equation:

⇒ y - 5 = 9x - 9,

⇒ y = 9x - 4,

Therefore, the required equation of tangent-line is y = 9x - 4.

Learn more about Tangent Line here

https://brainly.com/question/31617205

#SPJ3

Solve the equation to find a positive value of c:
62 + 82 = c2
(20 points)

Answers

Answer:

The equation has 2 solutions

c = -12

c = 12

Step-by-step explanation:

Swap the sides

c² = 62 = 82

Simplify the equation

c² = 144

separate the solutions

c = ± 12

Solution

c = -12

c = 12

Please solve this. I need help on it​

Answers

Answer:

look at the photo............

9514 1404 393

Answer:

  ∠PTQ = 40°

  ∠PTR = 140°

Step-by-step explanation:

The two marked angles are "vertical" angles, so are congruent.

  ∠PTQ = ∠STR

  (x +28)° = (2x +16)°

  12 = x . . . . . . . . . . . . . . . divide by °, subtract x+16

Then the measure of angle PTQ is ...

  ∠PTQ = (x +28)° = (12 +28)° = 40°

That and angle PTR form a linear pair, so are supplementary.

  ∠PTR = 180° -∠PTQ = 180° -40° = 140°

What is the solution to the equation?
--23 = x – 18
х
Enter your answer in the box.

Answers

Answer:

x=-5

Step-by-step explanation:

move the x to the other side. Then move the - 23. you get -x=5

you divide by -1 and you get x=-5

Step-by-step explanation:

Given equation,

-23 = x - 18

⇛-23 + 18 = x

⇛ -5 = x

⇛x = -5 Ans.

Hence, the value of "x" is -5.

Dan received these tips in a given week. How much were his total tips.?

Answers

Answer:

we need the amount of tips to answer this ;-;

Step-by-step explanation:

Caleb wants to rent a kayak. Kayak rentals cost $91.61 for a half hour. If Caleb rents a kayak for 2.9 hours, how much will it cost him?

Answers

Answer:

$265.669

Step-by-step explanation:

$91.61 times 2.9 equals 265.669, therefore it would cost him $265.669. Round up/down if needed.

The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form.

Answers

Answer:

i need a picture or something man

Step-by-step explanation:

can somebody please help me asap

Answers

the slope is 2/3 and the y intercept is -3

Which of these provides the best evidence that an environmental change has occurred?

Answers

Answer:

after a dry periods lasting many years only a few individuals of a tree population survive and then produce drought tolerant offspring.

Step-by-step explanation:

Choose the BEST estimate!

Answers

Answer:

About 300 dollars

Step-by-step explanation:

THe best estimate for week one is 300, because 96 rounds to 100, and 100 * 3 equals 300.

The best estimate for week 2 is 600, because 204 rounds to 200, and 200 * 3 equals 600.

600 - 300 = 300, therefore the difference is about 300 dollars.

Hope this helps!

NEEDS HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

3

Step-by-step explanation:

w x and y are three integers w is 2 less than x y is 2 more than x prove that wy+ 4 =x^2

Answers

w + 2 = x

x + 2 = y

Cross multiply

y(w+2) = x(x+2)

wy + 2y = x^2 + 2x

make x the subject of the equation

x = y - 2

substitute this in place of (x) in 2x

wy + 2y = x^2 + 2(y-2)

wy + 2y = x^2 + 2y - 4

wy  + 2y - 2y + 4 = x^2

wy + 4 = x^2

Who does edge still in 2021?

Answers

Everyone uses this sofware to develop there decent knowledge about different courses that are best taught by Artificial Intelligence (A.I.).

ive been stuck for so long. pls help

Answers

Answer:

B

Step-by-step explanation:

Might be C, but I hope it helps

i will give brainliest to the best answer.

Answers

Answer:

Step-by-step explanation:

The slope intercept form is like so:

y = mx + b

mx is the slope

b is the y-intercept

Now in your equation:

y = 0.25x + 2

0.25x is the slope

2 is the y-intercept

Find the value of x. 2x – 15 – 7x + 24 = -36​

Answers

Answer:

9

Step-by-step explanation:

hlo!! dear!! glad to help u!

2x – 15 – 7x + 24 = -36​

2x -7x -15 +24= -36

-5 x + 9= -36

-5 x = -36-9

-5 x =-45

x = -45/-5

x = 8

thank u!!!

The number 62 is less than the number of tickets sold in a day at an amusement park. Which of the following inequalities represents the number of tickets sold in a day at the park?

A.
x > 62
B.
x < 62
C.
x = 62
D.
x < 64

Answers

Answer:

A

Step-by-step explanation:

because > means more than the other number

What are the leading coefficient and degree of the polynomial?
v +9-45-124

Answers

Answer

5x

Step-by-step explanation:

If x=47 , find the measures of angles 1,2 and 3​

Answers

Angle x and 2 are congruent so angle 2 is also 47 degrees.

Angle x and angle 1 are supplementary so angle x and angle 1 adds up to 180 degrees.

180-47=133. Angle 1 is equal to 133.

Angle 1 and angle 3 are congruent as well so angle 3 is also 133 degrees.

Which of the following inequalities is represented by the number line?
Question 9 options:

A)

x ≥ 1

B)

x < 1

C)

x > 1

D)

x ≤ 1

Answers

Solid dot with line (arrow) to right so A) x>= 1 is correct

Answer:

Step-by-step explanation:

x ≥ 1

Hope this helps!

close circle = ≥ or ≤

open circle = > or <

positive number = going to the right

negative number = going to the left

How do I solve 0.0055 m a cm ?

Answers

Answer:

863.83

Step-by-step explanation:

es por qué es un número multimedios y los los número se asen pares

dl

The number of marbles each sister gets when m marbles are shared equally among four sisters x = m/4

Answers

Answer:

m/4

Step-by-step explanation:

The zero of F -1(x) in F(x) = x + 3 is

-3
0
3

Answers

Answer:

The only zero of [tex]F^{-1}(x)[/tex] is [tex]3[/tex].

Step-by-step explanation:

The function [tex]F^{-1}[/tex] is the inverse of function [tex]F[/tex].

For a given [tex]x[/tex] and a given [tex]y[/tex], [tex]F^{-1}(y) = x[/tex] if and only if [tex]F(x) = y[/tex].

Let [tex]y[/tex] be a zero of [tex]F^{-1}(y)[/tex]. That is, [tex]F^{-1}(y) = 0[/tex].

By the reasoning above, since [tex]x = 0[/tex] and this particular [tex]y[/tex] satisfy [tex]F^{-1}(y) = x[/tex], it must be true that [tex]F(x) = y[/tex] for the same [tex]x = 0\![/tex] and [tex]y\![/tex].

Since [tex]x = 0[/tex] and [tex]F(x) = x + 3[/tex], [tex]F(0) = 3[/tex]. Therefore, [tex]y = F(0) = 3[/tex] since [tex]y = F(x)[/tex].

Thus, the zero of [tex]F^{-1}(y)[/tex] would be [tex]y = 3[/tex].


Find the perimeter of the
triangle.
16% + 16) cm
(9%-11) cm

Answers

Answer:

Step-by-step explanation:

Three equal sides, so lets find one by solving for x

6x + 16 = 9x-11

      -3x = -27

         x = 9

6(9) + 16 = 70

 9(9) - 11 = 70

70(3) = 210 cm

PLS HELP ILL GIVE BRANLIEST
What is the value of b in the equation (y^b)^4= 1/y^24?​

Answers

Answer:

b= -6

y^(b×4) = y^(-24)

b= -6

I need the answer ASAP

Answers

Answer:

Step-by-step explanation:

49 i Think I dont know but your part A is correct

Answer:

49 For sure is your answer

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