Question
Let $G$ be a group of order $p q$ where $p$ and $q$ are distinct primes and $p<q .$ Prove that the Sylow $q$ -subgroup is normal in $G$. (This exercise is referred to in this chapter.)
Step 1
The Sylow Theorems give us information about the number of Sylow $p$-subgroups and Sylow $q$-subgroups in $G$. In particular, we have: Show more…
Show all steps
Your feedback will help us improve your experience
Varsha Aggarwal and 53 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| = pqr where p, q, r are distinct primes. Show that G has a normal Sylow subgroup for either p, q or r.
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