Let H be a normal subgroup of a finite group G and let \(x \in G\) . If \(g c d ( | x | , | G / H | ) = 1\) , show that \(x \in H\) .
Elements of order coprime to $|G/H|$ lie in $H$
P-CH9S-061
- Area
- Algebra
- Status
- draft
P-CH9S-061
Let H be a normal subgroup of a finite group G and let \(x \in G\) . If \(g c d ( | x | , | G / H | ) = 1\) , show that \(x \in H\) .