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Hello all, I am a developmental math instructor, for now. I am a pure math graduate student.

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11 What is the kernel of a homomorphism? Feb 20 '15
9 Let R be a ring. Prove that if $x^2=x$ for each $x \in R$, then R is a commutative ring. [duplicate] Apr 20 '15
8 Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$ Oct 20 '13
8 Prove that a countable subset of $\mathbb{R}$ has Lebesgue outer measure zero Dec 8 '13
8 Show $\ker(\alpha)=\ker(\alpha)^2 \ \iff \ \ker(\alpha)\cap \mathrm{Im}(\alpha)=\{0\}$ Jun 24 '14
6 If a group $G$ contains an element a having exactly two conjugates, then $G$ has a proper normal subgroup $N \ne {e}$ Mar 11 '15
6 Let $S$ be a normal p-subgroup of a finite group $G$. Prove that $S \subseteq P$ for every Sylow p-subgroup $P$ of $G$ Mar 21 '15
5 What is a group action, and how can we apply it to Sylow theory Apr 6 '15
5 Evaluate the Cauchy Principal Value of $\int_{-\infty}^{\infty} \frac{\sin x}{x(x^2-2x+2)}dx$ Dec 10 '14
5 If $f:G \to H$ is a homomorphism with kernel $N$ and $K$ is a subgroup of $G$ then prove that $f^{-1}(f(K))=KN$ Feb 8 '15
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