List questions from cyclic-groups

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List Question

Why are these representations of $\mathbb Z_n$ not irreducible?

Is there a reliable method for finding irreducible subrepresentations in $GL(n,\mathbb R)$?

Comparing $\phi(\phi(n))$ and the number of elements in $(\mathbb{Z}/\phi(n)\mathbb{Z})^{\times}$ of order $\le \log(n)$

Prove that $H=\{a+b{\bf i} : a,b \in\mathbb Z\}$ is not cyclic.

If $t|k$ and $k|t$, why does $k=t$?

Finite subgroup proof

Computing left cosets in 10ℤ and dihedral group

Compute cosets in the dihedral group

how to show D is cyclic knowing it has a unique subgroup?

Number of decomposition in direct sum of cyclic groups

Number of elements in direct product of two groups

is the group cyclic, if Normal Subgroup and Quotient group are cyclic.

How many elements of order 2 in a group of order 16 generated by two elements

How Cyclic Group of order 6 is isomorphic to the product of cyclic groups of order 2 and 3. How to generalize this.

Orbits of rotations under action by D4.

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