Symmetry groups and Caley tables

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SUMMARY

The discussion centers on constructing the symmetry group and Cayley table for a shape with rotational symmetry but no reflectional symmetry, specifically an odd star shape. The user seeks clarification on standard notation for symmetry groups, questioning if it should be represented as S(Q) = {e, Rπ/2, Rπ, ...}. The response confirms that the Cayley table should be constructed with elements listed across the top and down the side, calculated through composition of symmetries. It emphasizes the importance of adhering to the notation specified in the user's course materials.

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  • Knowledge of standard notation in group theory
  • Ability to construct and interpret Cayley tables
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Students of mathematics, particularly those studying group theory, geometry, or symmetry, as well as educators seeking to clarify concepts related to symmetry groups and Cayley tables.

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Homework Statement



I have a shape about the origin. It has rotational symmetry but not reflectional symmetry (its an odd star shape!).

I have to write down in standard notation the elements of the symmetry group and I have to construct a caley table under composition of symmetries.

I think I'm getting mixed up with some of the terminology here. By standard notation does it mean

S(Q) = {e, Rpi/2, Rpi,...) etc?

And the caley table under composition symmetries, does it mean simply the table constructed with each element across the top and down the side and then calculated in the normal way?

Thanks
 
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The definition of 'Standard notation' is almost certainly purely local, and definitely not standard. Sorry. You need to use whatever notation has been set in your book or lecture course.

The definition of Cayley table is precisely what you wrote.
 
Many thanx... Sometimes these maths books can be a bit vague
 

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