What does the notation S_4(2) mean?

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The notation S_4(2) refers to a specific group related to the symmetric group S_4, which encompasses all permutations of four objects. In this context, S_4(2) denotes a subgroup of S_4 that is associated with particular properties or structures within group theory. The discussion clarifies that S_4(2) and S_4(3) are not merely sequences or partial sums but represent distinct groups within the framework of permutation groups.

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  • Understanding of group theory concepts
  • Familiarity with symmetric groups, specifically S_n
  • Knowledge of permutation notation and operations
  • Basic comprehension of subgroup relationships
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krishna mohan
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Hi...

Could someone tell me what is meant by S_4 (2),S_4(3) etc? These are names of some groups...
 
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I believe it means a sequence at a certain number, partial sum.
 
No...not that..

This is in another context...these are names of some groups...It must mean that the group is related to S_4, the group of all permutations of 4 objects...
But I do not know what the relation is..
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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