Orthogonal group over finite field

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SUMMARY

The order of the orthogonal group O(n, F_q) over a finite field F_q can be calculated using established results found in literature, specifically referenced on Wikipedia. While this result is standard, it lacks comprehensive proofs in basic representation theory texts. The discussion suggests using induction over the dimension as a viable proof strategy. Further references or papers that detail this calculation are sought by participants in the forum.

PREREQUISITES
  • Understanding of orthogonal groups in linear algebra
  • Familiarity with finite fields, specifically F_q
  • Knowledge of representation theory fundamentals
  • Basic principles of mathematical induction
NEXT STEPS
  • Research the calculation of the order of orthogonal groups in "Representation Theory" by Fulton and Harris
  • Study the properties of finite fields in "Finite Fields" by Rudolf Lidl and Harald Niederreiter
  • Explore induction techniques in mathematical proofs
  • Review the Wikipedia page on orthogonal groups for additional context and references
USEFUL FOR

Mathematicians, particularly those specializing in group theory, representation theory, and finite fields, as well as students seeking to deepen their understanding of orthogonal groups.

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Let O(n,F_q) be the orthogonal group over finite field F_q. The question is how to calculate the order of the group.
The answer is given in http://en.wikipedia.org/wiki/Orthogonal_group#Over_finite_fields". This seems to be a standard result, but I could not find a proof for this in the basic representation theory books that I have. Neither could I solve it myself from the (direct sum) construction they have given.
Can someone please help me? It is enough if you give some references (books/papers) where it is solved.
 
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It is not within textbooks as it is comparably uninteresting. I recommend an induction over the dimension to prove it.
 

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