# Cohomology of $\text{PSL}_2(q)$

@article{Saunders2020CohomologyO, title={Cohomology of \$\text\{PSL\}_2(q)\$}, author={J. Saunders}, journal={arXiv: Representation Theory}, year={2020} }

In 2011, Guralnick and Tiep proved that if $G$ was a Chevalley group and $V$ an irreducible $G$-module in cross characteristic, then if $V^B = 0$, the dimension of $H^1(G,V)$ is determined by the structure of the permutation module on a Borel subgroup $B$ of $G$. We generalise this theorem to higher cohomology and an arbitrary finite group, so that if $H \leq G$ such that $O_{r'}(H) = O^r(H)$ then if $V^H = 0$ we show $\dim H^1(G,V)$ is determined by the structure of the permutation module on… CONTINUE READING

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