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 4 How do I find the number of group homomorphisms from $S_3$ to $\mathbb{Z}/6\mathbb{Z}$? 2 Prove that CX and CY are perpendicular 1 Given $G = (V,E)$, a planar, connected graph with cycles, Prove: $|E| \leq \frac{s}{s-2}(|V|-2)$. $s$ is the length of smallest cycle 1 Decomposing a subgroup 0 On Ceva's Theorem?

### Reputation (142)

 +50 How do I find the number of group homomorphisms from $S_3$ to $\mathbb{Z}/6\mathbb{Z}$? +15 How many elements of order d? +25 Given $G = (V,E)$, a planar, connected graph with cycles, Prove: $|E| \leq \frac{s}{s-2}(|V|-2)$. $s$ is the length of smallest cycle +5 How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$?

### Questions (3)

 3 How many elements of order d? 3 How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$? 0 Can any planar graph have 4 vertices and 4 regions?

### Tags (10)

 5 group-theory × 3 1 graph-theory × 2 4 abstract-algebra × 2 0 triangle 4 finite-groups 0 alternative-proof 2 geometry × 2 0 calculus 2 euclidean-geometry 0 discrete-mathematics

### Account (1)

 Mathematics 142 rep 15