AColoredReptile

### Questions (55)

 4 Suppose $N\trianglelefteq G$ and $H\leqslant G$. If $\vert G/N \vert$ is prime prove $H\subseteq N$ or $NH=G$ 4 If $G$ is a finite group and all non-identity elements of $G$ are order 2 then the product of these elements is the identity. 4 Homeomorphism between unit circle with point removed to real line. 3 Show that integral of $f$ over a manifold $M$ is independent of coordinate chart 3 Prove there is an open set $\widetilde W\subset W$ containing $q$ such that $\sigma(\widetilde W)$ is a smooth surface

### Reputation (408)

 +5 Number of cyclic subgroups of order $10$ in $\mathbb{Z}_{30}\oplus\mathbb{Z}_{120}$. +15 Show that integral of $f$ over a manifold $M$ is independent of coordinate chart +5 Show there is a countable collection of closed balls $\beta=\{B_n=\overline{B_{r_n}(x_n)}:n\in \mathbb{N}\}$ such that $U=\cup_nB_n^{\text{int}}$ +5 Compute $\int_C \frac{1}{1+\frac{z}{2}}dz$ where $C$ is the curve $\gamma(t)=(-2\sin t,2\cos t,2t^2)$ for $t\in[0,1]$

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### Tags (35)

 0 multivariable-calculus × 19 0 linear-algebra × 6 0 proof-verification × 11 0 general-topology × 4 0 differential-geometry × 8 0 calculus × 3 0 group-theory × 7 0 elementary-set-theory × 3 0 real-analysis × 7 0 derivatives × 2

### Account (1)

 Mathematics 408 rep 210