Sequence of Integers defining Abelian Group/Examples/Order 100

Examples of Sequences of Integers defining Abelian Groups

Let $G$ be an abelian group of order $100$.

From Sequence of Integers defining Abelian Group, $G$ can be expressed in the form:

$G = C_{n_1} C_{n_2} \cdots C_{n_r}$

The possible sequences $\tuple {n_1, n_2, \ldots n_r}$ of positive integers which can define $G$ are:

 $\ds r = 1:$  $\ds \tuple {100}$ $\ds r = 2:$  $\ds \tuple {50, 2}$ $\ds$  $\ds \tuple {20, 5}$ $\ds$  $\ds \tuple {10, 10}$

Proof

Determined by inspection.

$\blacksquare$