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

How are different types of linear equations similar and how are they different

Answers

Answer:

The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.

Step-by-step explanation:

The center of the circle whose equation is (x + 2)² + (y - 3)² = 25 is

Answers

Answer:

The center of the circle is at: C=(−2,3).

The radius of the circle is r=5.

Step-by-step explanation:

A circle with center at (h,k) and a radius of r has equation (x−h)2+(y−k)2=r2.

In this example our circle equation can be written as:

(x−(−2))2+(y−3)2=(5)2

So, we have: h=−2 , k=3 and r=5.

select “equivalent” or “not equivalent” to indicate whether the expression above is equivalent or not equivalent to the values or expressions in the last column

Answers

9514 1404 393

Answer:

EquivalentNot EquivalentEquivalentNot Equivalent

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

__

The left-side expressions (all the same) can be simplified to ...

  (7^(1/5))·(49^(7/5)) = (7^(1/5))·((7^2)^(7/5))

  = (7^(1/5))·(7^(14/5)) . . . . . . matches 3rd right-side expression

  = 7^(1/5 +14/5) = 7^(15/5) = 7^3

  = 343 . . . . . . . . . . . . . . . . . . matches 1st right-side expression

__

49 is obviously not equivalent to 343.

49^(2/10) is obviously not equivalent to 49^(7/5).

If AB= 4 units and DC=4 units , what is the length of BC​

Answers

Answer:

sqrt(2)

Step-by-step explanation:

bd=ab/2=2

=> bc=qrt(bd^2+dc^2)=sqrt(4+16)=2sqrt(5)

2
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The numbers 7. 11, 12, 13, 14, 18, 21, 23, 27 and 29 are written on separate cards, and the cards are placed on a table with the numbers facing
down.
The probability of picking a card with an even number is?

Answers

Answer:

Answer=3/10

Step-by-step explanation:

even numbers=3

total cards=10

P=number of possible outcomes/total outcomes

=3/10

Answer:

you have a 3/10 probability of geting a even number bc

Step-by-step explanation:

there are ten numbers shown in the question and there are three even numbers out of ten so that is how you get you anewer

TIME REMAININO
58:40
Which graph could represent a constant balance in a bank account over time?
Daily Balance
Daily Balance
Daily Balance
de
10
$
1378
Time (day)
1 2 3 4 5
Time day)
O
Daily Balance
35
Save and Exit
NE
Suband
Mark this and return

Answers

Dalit balance
Thanks hope you have a good day

What is the solution to the system of equations grahped below

Answers

Because the the two lines cross (1,4), that is the solution. D is correct!

Please help with this

Answers

Answer:

697.24 and 886.76

Step-by-step explanation:

792+.92*103= 886.76

792-.92*103= 697.24

if that's not correct try 697.76 and 886.25

Dan ate 6/7 of a Snickers, Ariel ate 3/4 of a similar Snicker, who ate the most? (Write the name in the blank)

Answers

Answer:

dan

Step-by-step explanation:

to find out which person ate more, you have to convert the fractions into ones with the same denominator, or bottom number

the lcf (least common factor) of 7 and 4 is 28

6/7 * 4/4 = 24/28

3/4 * 7/7 = 21/28

using these numbers we can tell that dan ate more

Simplify the following:

[tex]\sqrt{50} x^{2} y^{3}[/tex]

Answers

Answer:

5xy[tex]\sqrt{2y}[/tex]

Step-by-step explanation:

Answer: simplify

5√2x² y²

A.4/10
B.1/20
C.3/40
D.2/20

Answers

Answer:

it's C. 3/40

Step-by-step explanation:

ghjfrukkbf


Will mark as brainlist answer quickly



Which one of the following is the same as 72 dekaliters ?


A. 72 dal


B. 72 dI


C. 72 deciliters


D. 72 ml

Answers

Answer:

72 dal

Step-by-step explanation:

short form to dekaliter is dal

Based on the abbreviations for various units of measurements, the best answer here is A. 72 dal

Units of measurements have shorter forms such as:

Liters ⇒ LMilliliter ⇒ MLDekaliters ⇒ DAL

As the short form of dekaliter is dal, the first option must be correct as it is the same as 72 dekaliters albeit in a shortened form.

We can therefore conclude that 72 dal and 72 dekaliters are the same.

Find out more at https://brainly.com/question/15998529.

Find the missing lengths of the sides.

Answers

Answer:

I would go with 3rd option

I used Pythagorean Theorem and my answer is that

a=3sqrt3

b=3

Step-by-step explanation:

Not sure why it's backwards I checked and rechecked, so let me know.

Please answer this hurry!!!!!

Answers

The answer is d, y = -x + 5.

Ed bought cupcakes for his sister's birthday party.42 cupcakes had sprinkles on top. The other 33 cupcakes did not have sprinkles. What percentage of the cupcakes had sprinkles?

Answers

Answer:50000000000000000000000000000000000000000000000000000

Find the area of the parallelogram.

Answers

Answer:

894

Step-by-step explanation:


If you were to rotate ABCD 180° about the origin, what would the coordinate of A' be?

-5 -5
-3 -5
-5 -3
-3 3

Answers

Answer:

(-3,-5) .............................

How to solve this?With solutions

Answers

Answer:

C

Step-by-step explanation:

Step 1: Determine the value of x by using [tex]x=tan^{-1}(\frac{\sqrt{3} }{\sqrt{2}} )[/tex]

[tex]x=tan^{-1}(\frac{\sqrt{3}}{\sqrt{2} })=50.7685 degrees[/tex]

Step 2: Substitute x=50.7685 degrees into the original equation

[tex]2cos^{4}(x)-sin(x)=2cos^{4} (50.7685)-sin(50.7685)=0.320-0.7746=-0.4546[/tex]

Please help me with this question❤️ thanks

Answers

Answer:

70

Step-by-step explanation:

that can be 30 ft

Mike jogged a total distance of 5 and 1 over 3 miles during the months of October and November. If Mike only jogged 1 over 6 mile every day, which expression shows the number of days in which he went jogging?

5 and 1 over 3 multiplied by 1 over 6
5 and 1 over 3 plus 1 over 6
5 and 1 over 3 minus 1 over 6
5 and 1 over 3 divided by 1 over 6

HELP MEH PLZ !!! IT'S (15 POINTS) T^T

Answers

Answer:

Step-by-step explanation:

5 1/3 x 1/6 = 8/9

5 1/3 + 1/6 = 5 2/6

5 1/3 - 1/6 = 31/6

5 1/3 / 1/6 = 32

Answer:

the correct answer for this problem is D: 5 and 1/3 divided by 1/6

Step-by-step explanation:

please be super quick 3 minutessssss

Answers

Answer:

im pretty sure its B

Step-by-step explanation:

I THINK SOOO AHH

Are 3and 9 divisible by 27,621

Answers

Answer:

yes

Step-by-step explanation:

If x varies directly as y,and x=18x=18when y=3.6,what is x when y=12

Answers

Answer:

x = 60

Step-by-step explanation:

Write an equation using the ratio between x and y:

18/3.6 = x/12 Multiply both sides by 12:

216/3.6 = x

60 = x

Question 18
Calculate the mean 12, 2, 9,

12, 10

Answers

Answer:

Mean = 9

Step-by-step explanation:

The mean is the average of a data set.  Given the values, 2, 9, 10, 12, 12:

Add all the numbers in the data set, and divide its sum by the number of items in the set:

Mean = [tex]\frac{2+9+10+12+12}{5}[/tex] =  [tex]\frac{45}{5}[/tex] = 9

Therefore, the mean of the given data set is 9.

solve pls branliest !

Answers

Answer:

72

Step-by-step explanation:

8×3²

=8×9

=72

so it is the answer

Original remains fossils have been protected from decay by amber, permafrost, oil, and _____.

sediment
wood
weather
coal

Answers

Answer:As I know the answer is coal

Step-by-step explanation:

Please votes me 5 stars,1 hearts and mark as Brainliest for me .Thanks

help pls!!
#420hehsh

Answers

Answer:

It's gonna be probably A

fill in the blank (Geometry B)

Answers

Step-by-step explanation:

ratio

to

sind = d/e

sinf = f/e

What is the dependent quantity?
A) types of food I eat
B) not enough information
C) cholesterol levels

Answers

Answer?: I believe its C

No Explanation Because No

Answer: C is the answer

Step-by-step explanation:

Plz help me
I will thank you

Answers

Answer:  89674 buckets were produced in 4 months

Answer:

Step-by-step explanation:

First you have to do 5263 / 7 = 751.9 (rounded 751.857143)

Then do 751.9x121.6= 91 431

You get 121.6 because that is how many days are in 4 months.

Hope this helps !!!!

Have a good day/night!!<333

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