### Subgrpous

Prove: any subgroup of the order of p^(n-1) in a group of order p^n, where p is a prime, is a normal subgroup

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

Prove: any subgroup of the order of p^(n-1) in a group of order p^n, where p is a prime, is a normal subgroup

The following is is meant to have some assumptions made (like "n"). I have been up all night trying to figure this out. It can't be Euler because the vertices can't be >1. It might be Hamilton if I assume that E of G(V,E) is infinte..but how would I get my answer? I would just have sets (e1, e2,...) Could this be a straight

Let SIGMA = {a,b} be an alphabet. a. List between braces the elemnts of SIGMA4. the set of strings of length over SIGMA. b. Let A = SIGMA1 U SIGMA2 and B = SIGMA3 U SIGMA4. Describe A, B and AUB in plain English.

Give an example of or else prove that there are no relations on {1,2} that is symmetric and transitive, but not reflexive.

Give an example of or else prove that there are no relations on {a,b,c} that is reflexive and transitive, but not antisymmetric.

Determine whether the binary relation R on Z, where aRb means a^2 = b^2, is reflexive, symmetric, antisymmetric, and/or transitive.

Find the value and the optimal strategies for the two person zero-sum game below. Player 2 Player 1 1 2 3 2 0 3 I have determined the value of the game, but I don't know how to get to the optimal strategy. Please step through. My professor gave us the answer: Row Player Value = 4/3, The optimal strategy for the ro

A. Write the first 6 elements of the following sets: E is the set of even numbers E={ } L is the set of numbers divisble by 11. L={ } S is the set of numbers divisible by 6. S={ } b. Draw a Venn Diagram to represent the relationship among E,L,S. c. Place the following five numbers on the V

The attached file has a problem that I can't figure out how to set up. Can you take a look and explain how this problem should be set up? There are two people playing a two-person constant-sum game. Player 1 wants to travel from New York to Dallas using the shortest of the possible routes listed below. Player 2 has the ab

To prove that a statement of the form "If P then Q", you may assume that: A. P=Q B. P is true C. Q is true D. P is false E. nothing until it has been proved

To prove a statement "If P then Q", it is valid to prove which of the following statements instead? A. If not Q then not P B. If Q then P C. If not P then not Q D. Q only if P E. Both P and Q are true

A traveler owing a gold chain with 7 links is accepted at an inn on condition that he pay one link of the chain for each day he stays. if the traveler is to pay daily and may be given links already used in payment as change, show that he only needs to take out one of the links of the chain in order to pay each day for 7 days. (n

Please see attached pdf

Given S is a subset of R Suppose S' (set of all accumulation points in S) = emptyset Prove S is countable. I think I am supposed to use the Bolzano-Weierstrass Theorem but I can't figure out how to apply it.

Given the universal set of {x 0<x< 10}(this should read less than and equal too) and sets A,B,and C as defined below: A={factors of 6) B= {factors of 10} C= {odd numbers} a. List the elements in A U B U C. (they are suppossed to be upside down U"s ) b. State A U (B U C). (the U in between the b, c is the wrong way).

We say that an event A E A is nearly certain if A is nearly certainly equal to OMEGA. In other words, OMEGA = AUN , where N is a negligeable set.

Please see the attached file for the fully formatted problems. Let (Omega, A, P) be a probability space. We consider a series of mesurable sets (An)nEnCA . Prove that P(lim infnAn).... Prove that if the series is convergent, we have continuity, i.e. ...

Please see the attached file for the fully formatted problems. Let (Omega, A) be a measurable space, and P:A--> [0,infinity] an application such that P(AUB) = P(A) + P(B) when A,B E A and A intersection B = ø, and P(Omega) = 1 . Prove that the following statements are equivalent: (i) P is a probability (ii) P is continuou

Please see the attached file for full problem description. Let be a probability set. Prove that if is a family of events, then for all ,

Please see the attached file for full problem description with proper symbols. --- Let A and B be two events such that P(A) = 3/4 and P(B) = 1/3. Prove that 1/12=<P(A intersection B)=<1/3 and give two examples where these limits are reached. In the same way, find an interval for P(AUB) .

If A={1,3,4}, B={2,4,6,8), C=(1,4,5} and the universe is the counting numbers less than, then find the following: A. AUB(B has line over it) B. AU(BnC)

(A union B)* = (A*B*)* = (A* union B*)*

Let S be a set with an associative binary operation but with no identity. Choose an element 1 not belonging to S, write M = {1} or S, and define an operation on M by using the operation of S and 1s=s=s1 for all s belonging to S. Show that M is a monoid.

Problem: A company makes cameras. The price per camera at which x million cameras can be sold is: p(x) = 94.8 - 5x. 0 -< x -< 15 (the symbol -< is the "greater or equal to sign", I couldn't get it to work on my computer) The cost of making x million cameras is: c(x) = 156 + 19.7x (x is in millions of

Note. I don't how to make a letter with a line overtop of it so the equivalent notation here is *. ex) a* = a bar (a with a line overtop of it) Let M be a commutative monoid. Define a relation ~ on M by a ~ b if a = bu for some unit u. (a) Show that ~ is an equivalence on M and if a* deontes the equivalence class of a, let

An element e of a monoid M is called an idempotent if e^2 = e. If M is finite, show that some positive power of every element is an idempotent.

Consider the Cayley table: (see file) Show that there is only one way to complete table (1) so that the resulting operation is associative, and that the result makes {a,b} into a commutative monoid.

Solve the following equation SEND + MORE = MONEY where each letter stands for a digit between 0 - 9 and each digit can only be used once. clues: M = 1 and O = zero

Show that there are no "prime triplets", that is numbers p, p+2, p+4, that are primes other than 3,5,7.

Use the euclidean algorithm to find the greatest common divisor of 981 and 1234.