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# abstract algebra代写|Group Theory代写|抽象代数代写|陪集代写

Abstract algebra不算是一门简单的学科，这门学科在国内叫做抽象代数，经常有很多学生在学linear algebra或者analysis(advance calculus)的时候觉得并不困难，但是却觉得Abstract algebra很难，这是因为没有找到正确的方法学习Abstract algebra，UpriviateTA有一系列非常擅长Abstract algebra的老师，可以确保您在Abstract algebra取得满意的成绩。

$$N=\bigcap_{x \in G} x H x^{-1}$$

Here is some extra practice with left cosets of various subgroups. Let $H$ and $K$ be subgroups of $G,$ and consider the map $f$ which assigns to the coset $g(H \cap K)$ the pair of cosets $(g H, g K)$. Show that $f$ is well-defined and injective, and therefore
$$[G: H \cap K] \leq[G: H][G: K]$$
Thus (Poincaré) the intersection of finitely many subgroups of finite index also has finite index.

$g_{1}(H \cap K)=g_{2}(H \cap K)$ iff $g_{2}^{-1} g_{1} \in H \cap K$ iff $g_{1} H=g_{2} H$ and $g_{1} K=g_{2} K,$ proving
both assertions.

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