Projective symplectic group

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Definition

Let m be a positive integer and K be any field. The projective symplectic group PSp(2m,k) or PSp_{2m}(K) is defined in the following equivalent ways:

For a prime power q, we denote by PSp(2m,q) the group PSp(2m,\mathbb{F}_q) where \mathbb{F}_q is the (unique up to isomorphism) field of size q.

Chevalley notation

The projective symplectic group PSp(2m,K) is the Chevalley group of type C, denoted C_m(K). Note that the degree parameter when describing it as a Chevalley group is half the size of the matrices.

For a prime power q, we denote by C_m(q) the group C_m(\mathbb{F}_q) where \mathbb{F}_q is the (unique up to isomorphism) field of size q.

Facts

Collisions with other Chevalley groups

Simplicity