I'm missing something here. Let X = <mo fence="false" stretchy="false">{ <mo stretchy="

Perla Galloway 2022-04-30 Answered
I'm missing something here. Let X = { ( 123 ) , ( 132 ) , ( 124 ) , ( 142 ) , ( 134 ) , ( 143 ) , ( 234 ) , ( 243 ) }, A 4 act on X by conjugation (inner automorphisms) and x = ( 123 ), then 4 = | O ( x ) | = | G | / | G x | = 12 / | G x | . However, G x = { 1 }
What's wrong here?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Litzy Fuentes
Answered 2022-05-01 Author has 22 answers
The stabilizer is not the identity, because your action in conjugation, not multiplication. Every group element stabilizes itself under conjugation, and every power of a group element stabilizes the original element, too.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2022-05-03
A stained glass window consists of nine squares of glass in a 3x3 array. Of the nine squares, k are red, the rest blue. A set of windows is produced such that any possible window can be formed in just one way by rotating and/or turning over one of the windows in the set. Altogether there are more than 100 red squares in the set. Find k.
first, there are 8 Isometries of a square.
Identity, three rotations (90,-90,180) four reflections (vertical, horizontal, two diagonal axis). let G be the permutation group, then |G|=8, and I can find fix(g) for every g.
can someone give me a hint of how to proceed from there.
asked 2022-05-08
1. Sailing ships used to send messages with signal flags flown from their masts. How many different signals are possible with a set of four distinct flags if a minimum of two flags is used for each signals?
2. A Gr. 9 students may build a timetable by selecting one course for each period, with no duplication of courses. Period 1 must be science, geography, or physical education. Period 2 must be art, music, French, os business. Period 3 and 4 must be math or English. How many different timetables could a student choose?
asked 2022-05-09
Out of a group of 21 persons, 9 eat vegetables, 10 eat fish and 7 eat eggs. 5 persons eat all three. How many persons eat at least two out of the three dishes?

My approach: N ( A B C ) = N ( A ) + N ( B ) + N ( C ) N ( A B ) N ( A C ) N ( B C ) + N ( A B C )
21 = 9 + 10 + 7 N ( A B ) N ( A C ) N ( B C ) + 5
N ( A B ) + N ( A C ) + N ( B C ) = 10
Now the LHS has counted N ( A B C ) three times, so I will remove it two times as:-

Number of persons eating at least two dishes = N ( A B + B C + A C ) 2 N ( A B C ) = 10 2 5 = 0
Now it contradicts the questions that there are 5 eating all three dishes.
Is this anything wrong in my approach?
asked 2022-05-09
Let A and B be subsets of the finite set S with S = A B and A B = . Denote by P ( X ) the power set of X and denote by | Y | the number of elements in the set Y.
Given a statement | P ( A ) | + | P ( B ) | = | P ( A ) P ( B ) |
Use the Addition Counting Principle to prove or disprove the statement.

I understand that its asking me to find the elements of P ( A ) and P ( B ), but where does P ( X ) and | Y | fit in to solve this question?
asked 2022-05-02
Ministry of Education are inviting tender for four categories promoting the use of IT in education. Each category consists of 5, 4, 3, and 7 projects, respectively. Each project appears on exactly one category. How many possible projects are there to choose from? Explain your answer.
My Answer: ( 5 + 4 ) + ( 4 + 4 ) + ( 3 + 3 ) + ( 7 + 4 ) = 9 + 8 + 6 + 11 = 34 possible projects to choose from. I used the sum rule here.
Is this correct?
asked 2022-05-03
I am to create a six character password that consists of 2 lowercase letters and 4 numbers. The letters and numbers can be mixed up in any order and I can also repeat the same number and letter as well. How many possible passwords are there?
What I have pieced together so far:
Well, from the fundamental counting principle, we would definitely need 26 2 × 10 4 but obviously this is not all the possibilities since I can rearrange letters and numbers. Since it is a password the order matters so would I try and do a permuation of some sort like 6 P 2 since there are 6 slots to try to rearrange 2 objects (letters)?
asked 2022-04-30
I came across this question where I was asked to calculate the probability of drawing 2 identical socks from a drawer containing 24 socks (7 black, 8 blue, and 9 green). When solving this question, I tried tackling it using the counting principle directly as opposed to simply applying the combinatorics formula in hopes to get comfortable with that principle. Though, when I looked up the solution at the end of the book, the answer was completely different, and I am not sure why that is.

What I did was as follows: First, I noticed that when we draw the first sock, we have 24 different options to choose from and then only 1 in order to match it with the first one we chose. Then, I divided it by the total number of ways we can draw 2 socks out of 24 and got the expression:
24 1 24 23 = 1 23
The solution at the back of the book took care of each case separately (choosing 2 out of 7 blue socks, OR choosing 2 out of 8 blue socks OR choosing 2 out of 9 green socks), which makes sense, but what is wrong with my approach?