How to prove Cs is a subgroup of C3v?

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To prove that Cs is a subgroup of C3v, it is essential to establish whether C3v contains an element of order 2. The Cs group consists of two elements: the identity E and the reflection operator C_sigma. The discussion highlights that C_sigma, a plane reflection operator, does not appear to exist within the C3v group. If C3v does indeed have an element of order 2, then it can be concluded that Cs is isomorphic to a subgroup of C3v. Understanding the structure of these groups is crucial for the proof.
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Homework Statement


prove that Cs is a subgroup of C3v group


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The Attempt at a Solution


There are only two elements in Cs group, E and C_sigma. C_sigma is plane reflection operator which does not seem to exist in C3v group. This leads to my question here.
 
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Does C3v contain an element of order 2? If so it has a subgroup isomorphic to Cs.
 
pasmith said:
Does C3v contain an element of order 2? If so it has a subgroup isomorphic to Cs.
Thanks, this makes sense!
 

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