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Results tagged with symplectic-group
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user 35840
12
votes
Accepted
Structure of symplectic group over finite fields
You can find tables of the maximal subgroups of all (almost) simple classical groups in dimensions up to $12$ in the book:
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, John N …
- 37.4k
14
votes
Accepted
Symplectic groups $Sp_{2m}(2)$ as $2$-transitive permutation (i.e. Galois) groups
Both of these actions are 2-primitive, so the 1-point stabilizer acts primitively on the remaining points.
The 1-point stabilizers in the two actions are the orthogonal groups ${\rm SO}^{\pm}_{2m}(q) …
- 37.4k
4
votes
Accepted
Normalisers and stabilisers in classical groups $\operatorname{PGL}_{4}$
The difference between the examples arises principally because $5 \equiv 1 \bmod 4$ and $3 \equiv 3 \bmod 4$.
For $q \equiv 1 \bmod 4$, $G := {\rm GL}(4,q)$ has centre $Z$ divisible by $4$, and conta …
- 37.4k