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.

$\blacksquare$

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $14$: The classification of finite abelian groups: Example $14.1$