Question
Suppose that $K$ is a proper subgroup of $H$ and $H$ is a proper subgroup of $G$. If $|K|=42$ and $|G|=420$, what are the possible orders of $H ?$
Step 1
We have \( |K| = 42 \) and \( |G| = 420 \). Since \( K \) is a subgroup of \( H \) and \( H \) is a subgroup of \( G \), the order of \( H \) must be a multiple of the order of \( K \) and must also divide the order of \( G \). 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
Suppose that K is a proper subgroup of H and H is a proper subgroup of G. If |K| = 42 and |G| = 420, what are the possible orders of H?
Let $G$ be an abelian group. Let $H$ be a subgroup of $G$, and let $K=\left\{x \in G: x^{2} \in H\right\}$. Prove that $K$ 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