On the modular cohomology of $GL_2(\mathbb{Z}/p^n)$ and $SL_2(\mathbb{Z}/p^n)$

Let $p$ be an odd prime. Denote a Sylow $p$ -subgroup of $G L_{2} (Z / p^{n})$ and $S L_{2} (Z / p^{n})$ by $S_{p} (n, G L)$ and $S_{p} (n, S L)$ respectively. The theory of stable elements tells us that the mod- $p$ cohomology of a finite group is given by the stable elements of the mod- $p$ cohomology of it’s Sylow $p$ -subgroup. We prove that for suitable group extensions of $S_{p} (n, G L)$ and $S_{p} (n, S L)$ the $E_{2}$ -page of the Lyndon-Hochschild-Serre spectral sequence associated to these extensions does not depend on $n > 1$ . Finally, we use the theory of fusion systems to describe the ring of stable elements.

On the modular cohomology of $G L_{2} (Z / p^{n})$ and $S L_{2} (Z / p^{n})$

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On the modular cohomology of $G L_{2} (Z / p^{n})$ and $S L_{2} (Z / p^{n})$

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On the modular cohomology of GL2(Z/pn)GL2​(Z/pn) and SL2(Z/pn)SL2​(Z/pn)

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On the modular cohomology of GL2(Z/pn)GL2​(Z/pn) and SL2(Z/pn)SL2​(Z/pn)

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On the modular cohomology of $G L_{2} (Z / p^{n})$ and $S L_{2} (Z / p^{n})$

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On the modular cohomology of $G L_{2} (Z / p^{n})$ and $S L_{2} (Z / p^{n})$

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