Definition:Nu Function

Definition

The $\nu$ (nu) function is the function $\nu: \Z_{>0} \to \Z_{>0}$ is defined as:

$\forall n \in \Z_{>0}: \map \nu n = $ the number of types of group of order $n$

Sequence of $\nu$ Function

The sequence of values of $\nu$ function: $\map \nu n$ for $n = 1, 2, 3, \ldots$ begins:

$1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2, 5, 4, 1, 4, 1, 51, 1, 2, 1, 14, 1, 2, 2, 14, \ldots$

Also see

• Finite Number of Groups of Given Finite Order: $\map \nu n$ is finite for any given $n \in \Z_{>0}$.

• Results about the $\nu$ function can be found here.

Linguistic Note

$\nu$ is the $13$th letter of the Greek alphabet and voiced nu (pronounced new).

Sources

• 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $1$: Introduction to Finite Group Theory