if g % h is cyclic, prove that g and h are cyclic. state the general case.

Answers

Answer 1

The general case when G₁⊕G₂⊕G₃...⊕Gₙ is cyclic generated by (g₁, g₂, g₃,...,gₙ) is that the subgroups G₁, G₂, G₃,...., Gₙ are cyclic generated by  g₁, g₂, g₃, ..., gₙ respectively.

G⊕H is cyclic

That is G⊕H = <(g, h)>

Let us choose an arbitrary element g₁ ∈ G, then as G⊕H is cyclic

(g₁, h₁) ∈ G⊕H = <( g, h)>

This means that there exists an integer x such that

(g₁, h₁) = (g, h)ˣ

(g₁, h₁) = (gˣ, hˣ)

that is g₁ = gˣ

implies g₁ ∈ <g>

that is G ⊆ <g> as g₁ is an arbitrary element belonging to G

But we know <g> ⊆ G

Hence G = <g>

Thus G is a cyclic group generated by g.

Similarly we can prove that H group is cyclic generated by h, that is H = <h>

So the general case is that G₁⊕G₂⊕G₃...⊕Gₙ is cyclic generated by (g₁, g₂, g₃,...,gₙ), then the subgroups G₁, G₂, G₃,...., Gₙ are cyclic generated by  g₁, g₂, g₃, ..., gₙ respectively.

To know more on cyclic groups

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Related Questions

Wich measurement is the closest to the area of the triangle in square centimeters???? :(

Answers

Jfkkdkdjemaaj
Dndndjjfkf
Jfkkfjf
Jfkkf

How much should Josea leave for the tip?
Reminder: The total bill was $38. She wanted to leave
a 15% tip.

Answers

Answer: soo if the bill is $38

then 15% times 100 = 0.15

38.00 x 0.15 = $5.7

Step-by-step explanation:

Answer:

$5.7 as a tip

Question Help
In the figure to the right, lines that appear to be tangent are tangent, and is the center of the circle.
What is the value of x?

Answers

Answer:

sorry

where is the figure

Hamburger Heaven is having a lunch special where customers buy one 1/4 pound cheeseburger and get one free. If they set aside 114 2/3 pounds of meat, how many -pound cheeseburgers can they make?

Answers

Answer: 459 cheeseburgers

Step-by-step explanation:

To find out the number of cheeseburgers that can be made, divide the amount of meat set aside by the amount of meat it takes to make one cheeseburger.

The amount of meat they have is:

= 114²/₃

= 344/3

Number of cheeseburgers is:

= 344/3 ÷ 1/4

= 344/3 * 4/1

= 1,376 / 3

= 458.67

= 459 cheeseburgers

The Raidius of a spherical globe is 9 inches what is the volume of the globe? ​

Answers

Answer: 3053.63


To get this you have 4/3 times pie times r3

write a propotion that can be obtained from the given figures. PLEAS ANSWER SENSIBLY​

Answers

Answer:

1.

(p+m)/m=(c+o)/o

or

m/(p+m)=o/(c+o)

2.a/v=s/i

or

v/a=i/s

What are the zeros for 3x^2 - 17x = -10? Below, you need to choose the correct factors and the correct zeros.

Answers

Answer:

Step-by-step explanation:

3x²-17x=-10

3x²-17x+10=0

3x²-2x-15x+10=0

x(3x-2)-5(3x-2)=0

(3x-2)(x-5)=0

3x-2=0,x=2/3

x-5=0,x=5

How can you convince someone that 8^0=1?

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{Fun fact: ANY NUMBER that is raised to the power of 0 is automatically}\\\large\textsf{equal to 1.. because the number to the 0 power is not a product of any}\\\large\textsf{number whatsoever, which why it has an understanding its recognition is 1. }[/tex]

[tex]\large\text{So, you can briefly tell them that for better understanding of exponents of}\\\large\text{0 that equals to 1}\uparrow[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

No links! Please!!

Factor 28x+12y using the GFC

Answers

Answer:

4(7x + 3y)

Step-by-step explanation:

28x+12y using GCF(greatest common factor)

gcf = 4

4(7x + 3y)

Answer:

4(7x+3y)

Step-by-step explanation:

28x+12y

Factor out the greatest commom factor  "4"

4(7x+3y) is the answer

The quotient of a number and -6 decreased by 2, is 10. FInd the number

Answers

Answer:

[tex]x = 48[/tex]

Step-by-step explanation:

Quotient means what you get when you divide a number by another number.

What we can do is make an equation using the information given, which turns out to be this:

[tex](\frac{x}{6}) - 2 = 10[/tex]

Add 2.

[tex]\frac{x}{6} = 8[/tex]

Multiply by 6.

[tex]x = 48[/tex]

Can someone please help me please I really need help please help me.

Answers

Answer:

Step-by-step explanation:

I can't get to act correctly either.

The answer is 1 day and 7 items.

Ariana

y = 5x + 2

Julie

y = 7x

The ys have to be the same so equate the right hand side.

7x = 5x + 2                      Subtract 5x from both sides.

7x - 5x = 5x - 5x + 2

2x = 2                             Divide by 2

2x/2 = 2/2

x = 1

1 day

7 items

20. 64% of the people at the movie theater bought popcorn in one weekend. For the next weekend, if the movie theater expects 125 people, then how many should be expected to buy popcorn?

Answers

Answer:

26

Step-by-step explanation:

20.64 divided by 100 then multiplied by 125 which will result in you receiving the answer 25.8 but I rounded it off to 26

!!!!!Please do step by step when answering!!!!!

Answers

Answer:

surface area =0.1357

Step-by-step explanation:

first, find the triangle area

to find use triangle area= base x height divided by 2

so .18 x .23

=0.0414

divided by 2

= .0207

multiplty 0.0414 by 4 because theres a total of 4 triangle sides

.0207 x 4 = 0.0828

now find the area of the square on the bottom

area= base x height

.23 x .23 = 0.0529

now add the two areas together

0.0529 + 0.0828= 0.1357

I will mark brainliest if you help me out and give me the correct awnser! Please help me with dot plotting.

Answers

Well, the median is 5

Anybody please help me

Answers

I believe the answer is a translation 4 units left and 1 unit up

pleas help meeeeeeeee !!

Answers

So for 9, to graph all you need to do is start at the origin (0,0) and go up 4 and over (right) 1.

AYUDAAAAA!!!
Partes de una cantidad
Es para hoy en la tarde porfis:-|​

Answers

Answer:

I don't speak Spanish sorry༼ つ ◕_◕ ༽つ/_ \

Gary is a regular customer at a coffee shop. The probablity that Gary orders a bagel is 85% . If Gary goes to the coffee shop 500 times, which is the best estimate for the number of times Gary will NOT order a bagel?

Answers

The answer will be 425................

find the value of each variable

Answers

Answer:

x=12.124

y=14

Step-by-step explanation:

tan(30)= 7/x

x= 7/tan(30)

sin(30)= 7/y

y= 7/sin(30)

A nursery owner buys 7 panes of glass to fix some damage to her greenhouse. The 7 panes cost
$15.05. Unfortunately, she bredks 3 more panes while repairing the damage. What is the cost of
another 3 panes of glass?

Answers

Answer:

Its 6.45

Step-by-step explanation:

we first need to know how much is one pane of glass so i divide

15.05÷ 7 and got $2.15

so each one pane of glass is $2.15

than i multiply 2.15 x 3 and got 6.45

So the cost is 6.45

A farmer sells 7.1 kilograms of pears and apples at the farmer's market. 1/4 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?

Answers

Answer:

your answer gonna be 4 1/10 that's your answer

5.325kg because 3/4 of the weight is apples and you take 1/4 away from 7.1. 1/4 of 7.1 is 1.775

How many grams is 3200 milligrams? A. 2.5 g B. 3 g C. 3.2 g D. 3.5 g

Answers

Answer:

C. 3.2g

Step-by-step explanation:

Mark Me Brainliest?

Answer:

3200mg is C; 3.2g


Word Problem #2
On one night, a scientist needs to determine the
distance she is away from the International Space
Station. At the specific time she is determining this the
space station distance they are both on the same line of
longitude 77' E. Furthermore, she is on a latitude of 29°
N and the space station is orbiting just above a latitude
of 61.4° N. In short, the central angle between the two
is 32.4°. If the Earth's radius is 3959 miles and the
space station orbits 205 miles above the surface of the
Earth, then how far is the scientist away from the space
station?
205 mi
3959 miles
324 CE
A
3959 miles

Answers

324 cececdcececececece

What is the measure in degrees of an angle that is supplementary to a 98
degree angle?

Answers

Answer:

82°

Explanation:

180 - 98 = 82°

The table shows a students results from spinning the pointer 30 times. Find the experimental probability that the pointer lands in a section with a number greater than or equal to 3.

Answers

Answer:

The answer is 8/15

hope it helps you

A car traveled 25 miles in 1/5 of an
hour. At the same speed, how many
miles will the car travel in 1 hour?

Answers

Answer:

in 1 hour it can travel 5(25)= 125 miles

Answer:

125 miles

Step-by-step explanation:

1/5 of a n hour = [tex]\frac{1}{5}*60[/tex] = 12 minutes

Distance traveled in 12 minutes (1/5 of an hour) = 25 miles

Distance traveled in 1 minutes = 25 ÷ 12 = [tex]\frac{25}{12}[/tex]

Distance traveled in 1 hour (60 minutes) = [tex]\frac{25}{12}*60 = 25*5 = 125 miles[/tex]

What theorem shows ACE = BCD

Answers

Answer:

SAS

Step-by-step explanation:

in two triangles

if EC=DC

AC =BC

M<ECA =M<DCB "V.O.A"

THEN triangle ACE = triangle BCD

The perimiter of a rectangle is 128 inches. The width of the rectangle is 4y inches. Find the length of the rectangle in terms of y.

PLEASE HELP!
I will give brainiest if it is correct

Answers

Answer:

The perimeter of a rectangle is 2W + 2L.

P = 2W + 2L

128 = 2(4y) + 2L = 8y + 2L

2L = 128 - 8y

L = 64 - 4y (this is the answer

Step-by-step explanation:

what is the formula to find the vertex of an exponential function?​

Answers

Answer:

formula: x = -b/2a

Step-by-step explanation:

25% of what number is 9​

Answers

Answer:

36

Step-by-step explanation:

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