If H and K are subgroups of G, show that H ∩ K is a subgroup of G. (Can you see that the same pr

Name: If H and K are subgroups of G, show that H ∩ K is a subgroup of G. (Can you see that the same proof shows that the intersection of any number of subgroups of G, finite or infinite, is again a subgroup of G ?)
Uploaded: 2023-09-05T17:05:19-08:00
Duration: 3 min 13 s
Channel: Claire Rochford
Description: If H and K are subgroups of G, show that H ∩ K is a subgroup of G. (Can you see that the same proof shows that the intersection of any number of subgroups of G, finite or infinite, is again a subgroup of G ?)

Question

Ahmet Yavas · Accepted Answer

1. First, we need to show that $H cap K$ is non-empty. Since $H$ and $K$ are subgroups of $G$,

Question

If $H$ and $K$ are subgroups of $G$, show that $H \cap K$ is a subgroup of $G$. (Can you see that the same proof shows that the intersection of any number of subgroups of $G$, finite or infinite, is again a subgroup of $G ?)$

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