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

NEED HELP ASAP WILL GIVE BRAINLIEST
Find the quotient: 11.28 divided by 4.7

Answers

Answer:

11.28 Divided by 4.7 equals 2.4.

Step-by-step explanation:

It's just simple division. Glad I could help though!

Answer:

2.4

Step-by-step explanation:

In one season a basketball player missed 45% of her free throws. How many free throws did she attempt if she made 176 free throws?

Answers

Step-by-step explanation:

she missed 45%, so that means she made 55% of her free throws.

and these 55% correlate to the absolute number of 176 successful throws.

so,

55% = 176

1% = 55%/55 = 176/55

100% = 1%×100 = 176×100/55 = 320

so, she attempted 320 free throws in total.

Why is it more difficult to get out of debt when only paying the minimum payment?
Your entire minimum payment goes toward principal and the interest continues to compound.
The majority of your minimum payment is going toward interest and finance charges and only a small amount toward the principal.
Your credit limit always resets, so you have a lot of spending power each month.

Answers

Answer:

The majority of your minimum payment is going toward interest and finance charges and only a small amount toward the principal.

Step-by-step explanation:

Can someone pls help me I really need help in here.. PLS…
And if u can explain how you make it I will appreciate it,. Thank u:(((

Answers

Answer:

So, "Compare the following rational numbers," its asking which of them is greater, or if there equal to each other.

So for 3.25 and 3 1/2

3 1/2 is greater

3.25 < 3 1/2 (so it should look like this when the symbol on that side)

and for -4.5 and -4.05

-4.05 is greater.

-4.5 < -4.05  (so the symbol is also on that side.)

2 (b) The line, L4, passes through the point (0,3)and is parallel to the line y - x + 3 = 0, find the equation of L4 -​

Answers

Answer:

y = x + 3

Step-by-step explanation:

→ Rewrite y - x + 3 = 0 in y = mx + c format

y = x - 3

→ Find the gradient of L4

1

→ Rewrite into y = mx + c format

y = x + c

→ Substitute in ( 0 , 3 )

3 = 0 + c

→ Find c

c = 3

→ Rewrite into y = mx + c

y = x + 3

Which equation represents the line that passes through C(2,4) and is perpendicular to the graph of y=1/3x-1?

Answers

Answer:

Step-by-step explanation:

y=-3x + b   the slope is the negative inverse of 1/3

4=3(2) + b

b =-2

the equation is

y=-3x - 2

slope is the negative inverse.  You find the y intercept, b, by plugging in the point (2,4) to get 4=3(2)+b

Stanley runs, swims, and bikes every day. During these workouts, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
Chapter Reference
e
What distance did Stanley cover while biking?

Answers

The time spent for each activity can be found writing an equation based on

the known parameters.

The duration of the time Stanley spent running is 1.5 hoursThe duration of the time Stanley spent swimming is 1 hourThe duration of the time Stanley spent Biking is 3 hours

The distance Stanley cover while biking is 48 miles

Reasons:

The running speed = 9 mph

The biking speed = 16 mph

Swimming speed = 2.5 mph

The time spent running = 0.5 hour + Time spent swimming

Biking time = 2 × Running time

The total distance covered = 64 miles

Required:

Time spent running, swimming, and biking

Solution:

Let t represent the time Stanley spent swimming, we have;

(t + 0.5)·9 + 2.5·t + 2×(t + 0.5)×16 = 64

43.5·t + 20.5 = 64

43.5·t  = 64 - 20.5 = 43.5

[tex]t = \dfrac{43.5}{43.5} = 1[/tex]

The time Stanley spent swimming, t = 1 hour

The time Stanley spent running = 0.5 + t

Therefore;

The time spent running = 0.5 hour + 1 hour = 1.5 hour

Time spent running = 1.5 hours

Time spent biking = 2 × Running time

Therefore;

Time spent biking = 2 × 1.5 hours = 3 hours

The distance Stanley cover while biking, d = 3 × 16 mph = 48 miles

Learn more here:

https://brainly.com/question/23206880

HELP LAST ATTEMPT!! marking as brainliest!

Answers

Answer:

i m not sure... whether it's correct or not......

bt I tried my best

Please help me with this question❤️ thanks

Answers

Answer:

70

Step-by-step explanation:

that can be 30 ft

−2/9−(−1/3÷3/5)

PLZZZZ ANSWER TEST

Answers

Answer:

The answer should be 1/3 Also known as 0.3333

P Simplify using
E
order of operations.
MD
AS
14 + 6 x 2 - 16 : 8
-
Enter
math

Answers

Answer:

Answer’s 43

Step-by-step explanation:

6+3=9

7(9)-4x5

63-4x5

63-20

Answer: 43

I need help in learning how to solve this equation using substitution:

-x -y -z = -8
-4x + 4y + 5z = 7
2x + 2z = 4

Answers

Answer:

x=3, z=-1, y=6

Step-by-step explanation:

you need to make the coefficients of each variable equal to each other then subtract 2 equations.

this one: multiply -4 in 1st

4x+4y+4z=32

-4x+4y+5z=7

_____________

8x+0-z=25

we have 2 equations with 2 variables now

2x+2z=4

8x-z=25

Im stuck on this anyone know it?

Answers

Answer:

The first one is correct

Step-by-step explanation:

I need to know if 3750 is right or wrong cause I think that’s the answer

Answers

It’s wrong.

The surface area means the area of the outside of the cube.

The area of a square is just width x height. And we are told one of the sides is 5.

A square has all equal sides. So what’s 5x5? then times that by the number of squares

I’ll put the answer in the comments

Find the difference. Simplify the
answer if possible.

15 9/15 - 11 1/3
A) 26 10/18
B) 4 4/15
C) -4 4/15
D) 4 8/12

Answers

D

Step-by-step explanation:

you subtract 15 and 11 = 4 then subtract 9-1 is 8 and then you find the common denominator

Solve for me please

Answers

Answer:

[tex]{ \rm{10x + 5y + 2z = 5}} \\ { \rm{4x - 5y - 5z = 8}} \\ { \rm{3x + 5y + 4z = 1}}[/tex]

• First find x

[tex]{ \rm{10x = 5 - 5y - 2z - - - (i)}}[/tex]

• Find y

[tex]{ \rm{4x = 8 + 5y + 5z - - - (ii)}}[/tex]

• Find z

[tex]{ \rm{3x = 1 - 5y - 4z - - - (iii)}}[/tex]

equate the three equations:

[tex]{ \rm{0z - 10= 2y}} \\ \\ { \boxed{ \bf{y = - 5}}}[/tex]

Find z

[tex]{ \rm{z = ( - 1 \times - 5)}} \\ \\ { \boxed{ \bf{z = 5}}}[/tex]

Find x

[tex]{ \rm{3x + 5y + 4z = 1}} \\ \\ { \rm{3x - 25 + 20 = 1}} \\ \\ { \rm{3x = 6}} \\ \\ { \boxed{ \bf{x = 2}}}[/tex]

Does anyone have the answer key for this assignment?

Answers

Answer:

try searching it up

Step-by-step explanation:

what is the midpoint of-2,2 4,-1

Answers

The midpoint is at (1, 0.5)

Rhombus PQRS with vertices P(-1,-3), Q(3,-4), R(4,-8) and S(0,-7)

A)Translation along the vector (4,10)
B) 90 (degrees) counterclockwise rotation about the origin.

Answers

A) Translation will slide all the points using the vector - add the vector to each point...
P’(3, 7), Q’(7, 6), R’(8, 2), S’(4, 3)

B) Rotation is tricky. 90 degrees will swap x with y and counterclockwise will reverse the sign of the new x
P’(-7, 3), Q’(-6, 7), R’(-2, 8), S’(-3, 4)

A clockwise rotation would swap the values and reverse the sign of the new y values
Half turn rotation would just reverse the values of all the coordinates

Mikey is reading a 604-page book. He read 148 pages last week. If he reads for x hours at 19 pages per hour, which equation represents how long it will take him to finish the book?


A.
148x + 19 = 604
B.
19x + 604 = 148
C.
19x + 148 = 604
D.
19x - 148 = 604

Answers

C plz put me brainliest

Answer:

C

Step-by-step explanation:

first take off the 148 of the 604 page book then divide the rest by 19 ,

it should be 24 hours - 1-day  .

it is c because it shows my explination because 19x + 148 is equal to 604 first take the 148 and 19 and x means multiplication so 19 times 24 = 456.

what is the most you would pay today for a promise to repay you $6,000 at the end of 6 years if your opportunity is 12%

Answers

Answer:

i need 9it

Step-by-step explanation:

ndbwsjl

Estimate the product 2.1 x 0.9

Answers

Answer:

2.0 estimated product

1.89 Actual product

Step-by-step explanation:

2.0*1.0=2.0

2.1*1.0=1.89

The product of 2.1 x 0.9 = 1.89

What is Product?

A product is something that has been multiplied one or more times. For instance, the mathematical formula "times equals" would be written with the terms "times," "multiplicand," and "product," respectively.

Given:

2.1 x 0.9

Now, Multiplying

                          2  .  1

                       x 0  .  9

                      _________

                           1  8  9

                           0  0  x

                      __________

                          1  .  8  9

Hence, the product of 2.1 x 0.9 = 1.89

Learn more about product here:

https://brainly.com/question/624355

#SPJ2

At a comic book convention vendor I was selling a set of 5 comics for $38.70.
Vendor 2 was selling a set of 4 comics for $30.76. Which vendor has the higher
unit price?

Answers

Answer:

Vendor I sells more by 0.05

Step-by-step explanation:

First, you do Vendor I, divide 38.70/5, which gives you $7.74.

Then, you go to Vendor 2, divide 30.76/4 and that makes the answer $7.69.

7.74 - 7.69 = 0.05

Vendor 1 has more then Vendor 2 by 5 cents.

Help help please please

Answers

Answer:

165km

Step-by-step explanation:

if 1cm on the map = 15km,

then since 11cm is 11x 1, we multiply the kilometers by 11, getting 165km.

What are the coordinates of the point?
(3,6)
(6, – 3)
(-3, -6)
(-3,6)

Answers

Answer:

The answer is D ( the last option in your list of possible answers. -3,6)

Answer:

(-3,6)

Step-by-step explanation:

It goes backwards 3 units to the left meaning the x value is negative 3. It goes up 6 meaning the y value is 6. Plug the values into (x,y) and you get (-3,6)

Simplify this please: ^4√y^20

Answers

Answer: y^5

Step-by-step explanation:

In the picture

solve pls brainliest

Answers

Answer:

Step-by-step explanation:

3.92,

8 + (-7) - (7) = 8 + 7 + (-4)​

Answers

Answer:

The inequality is false and equals -14=3

Step-by-step explanation:

You want to start by cancelling equal terms on both sides of the equation which means getting rid of both 8's. You are left with (-7)-(7)=7+(-4).

From here you want to solve both sides meaning adding -7-7 because both terms are negative they will combine, and the other side which is -7+4. They are opposite terms so you will subtract. This leaves you with -14=3 which is false.

list five rational numbers between -4/5 and -2/3 . Please tell by step by step explaintion ​

Answers

9514 1404 393

Answer:

  -0.67, -0.68, -0.69, -0.70, -0.71

Step-by-step explanation:

There are an infinite number of ways to do this.

Perhaps the simplest is to do it in decimal.

 -4/5 = -0.8

  -2/3 = -0.666... (repeating 6)

Any negative decimal number between these values will do. For example, ...

  -0.67, -0.68, -0.69, -0.70, -0.71

__

If you want to choose fractions that are evenly spaced between the given values, you can find their difference, then divide that difference into 6 parts (1 more than the number of numbers you need).

  -2/3 -(-4/5) = 4/5 -2/3 = (12 -10)/(5·3) = 2/15 . . . . length of interval

  1/6 of this difference is ...

     (1/6)(2/15) = 2/90 = 1/45

The interval end point nearest 0 is ...

  -2/3 = -30/45

so the 5 intermediate values will be that value with -1/45 repeatedly added:

  -31/45, -32/45, -33/45 = -11/15, -34/45, -35/45 = -7/9

_____

Additional comment

The fractions we came up with could be referred to as "5 arithmetic means between -2/3 and -4/5." There is nothing in the problem statement suggesting the values need to be evenly spaced.

When doing this in decimal, you can obtain a new value simply by adding more digits to the decimal fraction:

  -0.68, -0.685, -0.6853, -0.68531, -0.799

Suzy can type 85 words in 2 minutes. How many minutes will it take her to type her to type 500 word paper?​

Answers

Answer:

11,765

Step-by-step explanation: 1 word make up 0,024 minute so 500 words 500.0,024 = 11,765 minutes

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