Group cohomology of projective special linear group of degree two over a finite field

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This article gives specific information, namely, group cohomology, about a family of groups, namely: projective special linear group of degree two. This article restricts attention to the case where the underlying ring is a finite field.
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This article describes the group cohomology of the projective special linear group of degree two over a finite field. The order (size) of the field is q, and the characteristic prime is p. q is a power of p. We denote the group as PSL(2,q) or PSL_2(q).