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terrytao.wordpress.com | ||
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qchu.wordpress.com
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| | | | | In Part I we discussed some conceptual proofs of the Sylow theorems. Two of those proofs involve reducing the existence of Sylow subgroups to the existence of Sylow subgroups of $latex S_n$ and $latex GL_n(\mathbb{F}_p)$ respectively. The goal of this post is to understand the Sylow $latex p$-subgroups of $latex GL_n(\mathbb{F}_p)$ in more detail and... | |
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www.jeremykun.com
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| | | | | The First Isomorphism Theorem The meat of our last primer was a proof that quotient groups are well-defined. One important result that helps us compute groups is a very easy consequence of this well-definition. Recall that if $ G,H$ are groups and $ \varphi: G \to H$ is a group homomorphism, then the image of $ \varphi$ is a subgroup of $ H$. Also the kernel of $ \varphi$ is the normal subgroup of $ G$ consisting of the elements which are mapped to the identity under $ \varphi$. | |
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grossack.site
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| | | | | Chris Grossack's math blog and professional website. | |
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cosmiaineurope.wordpress.com
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| | | Cosmia's travel in Europe from June 2018 to July 2018 | ||
