Orbits

Question 1

Every permutation is a cycle.

Answer 1

False

Question 2

Every cycle is permutation

Answer 2

True

Question 3

The definition of even and odd permutation could have been given equally well before Theorem 9.15

Answer 3

False

Question 4

Every nontrivial subgroup H of S⁹ containing some odd permutation contains a transposition.

Answer 4

False

Question 5

A⁵ has 120 elements.

Answer 5

False

Question 6

Sn is not cyclic for any n>-1

Answer 6

False

Question 7

A³ is a commutative group

Answer 7

True

Question 8

S⁷ is isomorphic to the subgroup of all those elements of S⁸ that leave the number 8 fixed.

Answer 8

True

Question 9

S⁷ is isomorphic to the subgroup of all these elements of S⁸ that leave the number 5 fixed.

Answer 9

True

Question 10

The odd permutation in S⁸ form a subgroup of S⁸.

Answer 10

False