Question

An automorphism is an isomorphism from G to G where G is a group. Which of the following are automorphisms?
(a) T:x↦x−1.
(b) T:x↦x.
(c) T:x↦x2.
Option (a) and (b).​

Answer 1

Answer:

C )

Step-by-ste p explanation:

Answer 2

The correct answer is option (c) T:x↦x2.

Explanation:

• An automorphism is an isomorphism from G to G where G is a group.
• T:x↦x2 are automorphisms.
• In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
• It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure.
• The set of all automorphisms of an object forms a group, called the automorphism group.
• It is, loosely speaking, the symmetry group of the object.