Question

Let be a finite group of order at least two and let e denote the identity element of G. Let σ: G →g be a bijective group homomorphism that satisfies the following two conditions:
(i): if σ(g)=g for some gεG, then g=e,
(ii) (σ o σ) (g)=g for all g σ G.
The n which of the following is/are correct ?

• A. For each gεG, there exists hεG such that h-1σ(h)=g
• B. There exists xεG such that xσ(x)≠e.
• C. The map satisfies σ(x)-1 for everyone xεG
• D. The order of the group G is an odd number

Answer 1

Answer: (A), (C), (D)

For each gεG, there exists hεG such that h-1σ(h)=g

Answer 2

The correct options are: A, C and D