Let a be an element of a finite group G. The order of a is the
least power k such that ak = e.
Find the orders of following elements in S5
a. (1 2 3 )
b. (1 3 2 4)
c. (2 3) (1 4)
d. (1 2) (3 5 4)
Do you expect the ionization energies of anions of group 17
element to be lower than, higher than, or about the same for
neutral atoms of the same group?
Let B be a finite commutative group without an element of order
2. Show the mapping of b to b2 is an automorphism of B. However, if
|B| = infinity, does it still need to be an automorphism?
Use this theorem to find the inverse of the given matrix or show
that no inverse exists. (If an answer does not exist, enter DNE in
any cell.)
1
2
5
1
−1
0
2
1
2
1
−5
0
1
1
2
1
Let A = {1, 2, 3, 4, 5}. Find the inverse of the following
functions f: A→ A.
? = {(1,1),(2,3),(3,2),(4,4),(5,5)
? = {(1,5),(2,4),(3,2),(4,1),(5, 4)}
? = {(2,1),(3,4),(1,3),(4,1),(5, 2)}