Question
. If $N$ is a normal subgroup of $G$ and $|G / N|=m$, show that $x^{m} \in N$ for all $x$ in $G$
Step 1
We know that $N$ is a normal subgroup of $G$, so the quotient group $G/N$ is well-defined. Show more…
Show all steps
Your feedback will help us improve your experience
Varsha Aggarwal and 64 other Chemistry 101 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let G be a group with N is a normal subgroup of G. Assume [x,y]N = [xN,yN] and N is a subgroup of [G,G]. Prove that [G,G]/N = [G/N, G/N]
Let $G$ be an abelian group. Let $n$ be a fixed integer, and let $H=\left\{x \in G: x^{n}=e\right\}$. Prove that $H$ is a subgroup of $G$.
SUBGROUPS
C
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD