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# abstract algebra代写|group thoery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。

identity The identity element is the function $I: X \rightarrow G$ which is identically equal to the identity element, $e,$ of $G .$ Indeed, for any $f \in F$ and any $x \in X$ we have $(I * f)(x)=I(x) \cdot f(x)=e \cdot f(x)=f(x) .$ Hence, $I * f=f$.
inverse Let $f \in F$ be any element of $F .$ Let $g: X \rightarrow G$ be defined by $g(x):=$ $(f(x))^{-1}$. Then for any $x \in X$ we have $(g * f)(x)=g(x) \cdot f(x)=(f(x))^{-1}$. $f(x)=e=I(x) .$ Hence, $g * f=I$ so that $g$ is a left-inverse of $f$.
associativity Let $f, g,$ and $h$ be elements of $F$. For any $x \in X$ we have $f *(g * h)(x)=$ $f(x) \cdot(g * h)(x)=f(x) \cdot(g(x) \cdot h(x))=(f(x) \cdot g(x)) \cdot h(x)=(f * g)(x) \cdot h(x)=$
$(f * g) * h(x) .$ Hence, $f *(g * h)=(f * g) * h$

$a$ must be the identity element.

to one. Thus, $A$ does not have an inverse in $G$.

$$x \mapsto\left\{\begin{array}{l} x+4 \text { if } x<12 \\ x-12 \text { if } x \geq 12 \end{array}\right.$$
Show that $\sigma$ is a permutation and describe its orbits.

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