# Tagged Questions

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### Let $\,E = C([0, 1])$. Set $\,X =(E,||.||_\infty)$ and $\,Y =(E,||.||_1)$. …

Let $E = C([0, 1])$. Set $\,X =(E,||.||_\infty)$ and $\,Y =(E,||.||_1)$. Let us consider the identity $I :X→Y$. Prove that I is continuous and bijective. Calculate $\,||I||$. Prove that $I^{-1}$ is ...
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### Lie bracket of vector fields on $R^2$

Compute the Lie bracket$$\Big[-y\frac{\partial}{\partial x}+x\frac{\partial}{\partial y},\frac{\partial}{\partial x}\Big]$$ on $R^2$ Can you help me please?
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### An application of Sylow theorems in p-groups!

If $G$ is a finite group of order $p^{n}$ (which $p$ is a prime number) and have only one subgroup of order $p^{n-1}$ ,namely $H$ ,then $G$ is cyclic ! My "proof" is as follows: suppose $$x\in G-H$$ ...
### Show that if $m\in M_n$ and $k \in \Bbb Z_n$ then $mk\in M_n$.
Let $M_n = \{a\in \Bbb Z_n\mid \text{ there exists a non-zero integer$k$with the property that }a^k\equiv 0 \pmod n \}.$ Show that if $m \in M_n$ and $k \in \Bbb Z_n$, then $mk\in M_n$. For which ...