Menu Close

Let-G-be-a-finite-group-f-be-an-automorphism-of-G-such-that-f-x-x-x-e-Then-prove-that-i-g-G-x-G-such-that-g-x-1-f-x-ii-If-x-G-f-f-x-x-G-is-Abelian-

Tinku Tara 0 Comments
Pin




Question Number 193796 by Rajpurohith last updated on 20/Jun/23
Let G be a finite group,f be an automorphism of G such that f(x)=x ⇒x=e . Then prove that, (i)∀g∈G, ∃x∈G such that g=x^(−1) f(x). (ii)If ∀x∈G , f(f(x))=x ⇒ G is Abelian.
LetGbeafinitegroup,fbeanautomorphismofGsuchthatf(x)=x⇒x=e.Thenprovethat,(i)∀g∈G,∃x∈Gsuchthatg=x−1f(x).(ii)If∀x∈G,f(f(x))=x⇒GisAbelian.

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *