Question

Problem 3: (a) How many elements in S8 commute with the permutation (123)(45678)? (b) How many elements are there in S8 with order 15?

Answer #1

How many elements of the specified order does the given
permutation group have?
a) order 10 in S6
b) order 10 in S10

Let γ and δ be the following elements of the permutation group:γ
= (35412) δ = (314)(25).
a.) Calculate: (1) γ ◦ δ, (2) δ ◦ γ, (3) δ−1 and (4) γ−1.
b.) Do γ and δ commute?
c.) Prove that γ generates a group isomorphic to (Zn,+n) for some
n. d.) Prove that δ generates a group isomorphic to (Zn,+n) for
some n. e.) Prove that β = (123)(456) does not generate a group
isomorphic to (Zn, +n) for...

Problem 3 - use the following definition of permutation
below:
List A is a permutation of list B if any of the following are
true:
- list A and list B are both null, otherwise
- a.head=b.head, and a.tail is a permutation of b.tail
- a.head≠b.head, and there exists a list C such that
- a.tail is a permutation of b.head:c, and
- b.tail is a permutation of a.head:c
a) Use induction to prove that any finite list is a...

How many different elements does A × B have if A has 3 elements
and B has 2 elements?

how many molecules of S8 will be needed to produce 30.0g of S3O8
?

Given a random permutation of the elements of the set
{a,b,c,d,e}, let X equal the number of elements that are in their
original position (as listed). The moment generating function is X
is: M(t) = 44/120 + 45/120e^t + 20/120e^2t + 10/120e^3t+1/120e^5t
Explain Why there is not (e^4t) term in the moment generating
function of X ?

How many molecules are contained in each of the following
(scientific Notation)
2.66 mol S8
0.799 mol NH3
10.5 g of C2H5OH
1292 g of Cl2

How many electrons are needed for elements below to complete
thier octet?
a. group 1A elements
b. group 6A elements
c. group 5A elements
d.group 2A elements

How many elements does Z/4Z have?

The letters of the word “PROBLEM” are arranged in a random
order.
a. How many different arrangements are possible?
b. How many arrangements will start with “OE” or “EO”?
c. How many start with "M" and end with "P"?

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