MKS

### Questions (15)

 3 Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$ [duplicate] 2 Condition for three mutually perpendicular planes in 3D Geometry. 1 Prove that if a subgroup $H$ of a finite cyclic group $G=\langle a \rangle$ of order $n$ is generated by $a^m$, then $m$ is a divisor of $n$. 1 Does there exist an onto homomorphism from $(\mathbb{Z}_6,+)$ to $(\mathbb{Z}_4,+)$ and why? 1 Prove that $\int_{0}^{1}\frac{\log(1+x)}{1+x^2}\, dx=\frac{\pi}{8}\log 2$ [duplicate]

### Reputation (60)

 +18 Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$ +5 Prove that if a subgroup $H$ of a finite cyclic group $G=\langle a \rangle$ of order $n$ is generated by $a^m$, then $m$ is a divisor of $n$. +8 Does there exist an onto homomorphism from $(\mathbb{Z}_6,+)$ to $(\mathbb{Z}_4,+)$ and why? +5 Condition for three mutually perpendicular planes in 3D Geometry.

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### Tags (23)

 0 geometry × 3 0 plane-geometry × 2 0 3d × 3 0 group-homomorphism 0 group-theory × 3 0 abstract-algebra 0 cyclic-groups × 2 0 symmetric-groups 0 sequences-and-series × 2 0 normal-subgroups

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