Question

let G be a finite group of order n, let m be an integer such that gcd(m,n)= 1, show that if g∈G and g^m= e, then g=e

Name: let g be a finite group of order n let m be an integer such that gcdmn 1 show that if gg and gm e then ge 26955
Uploaded: 2024-11-06T23:41:56-08:00
Duration: 1 min 9 s
Channel: Hoan Nguyen
Description: let g be a finite group of order n let m be an integer such that gcdmn 1 show that if gg and gm e then ge 26955

          let G be a finite group of order n, let m be an integer such that gcd(m,n)= 1, show that if g∈G and g^m= e, then g=e

Added by Richard R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Hoan Nguyen

11/06/2024

Step 1

We have a finite group \( G \) with order \( n \), and an element \( g \in G \) such that \( g^m = e \), where \( e \) is the identity element of the group. We also know that \( \gcd(m, n) = 1 \). Show more…

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