Wikipedia claims that the group of units of Z24 (1,5,7,11,13,17,19,23), which all have order 2, and are isomorphic to (Z/2Z)^3 have an important connection to Monstrous Moonshine theory, however, I cannot find any other reference besides Wikipedia that claims this --- It was recommended on sci.math that I pose this question here.


Perhaps it's a mistake? And he meant that the primes of the Monster, which continue to 71, are what are considered in Moonshine.


Paul Hjelmstad, B.M, B.A.


[**Edit** (PLC): Here is the relevant passage from wikipedia:]



> 
> 24 is the highest number $n$ with the property that every element of the group of units $(\mathbb{Z}/n\mathbb{Z})^{\times}$ of the commutative ring $\mathbb{Z}/n\mathbb{Z}$, apart from the identity element, has order $2$; thus the multiplicative group $(\mathbb{Z}/24\mathbb{Z})^{\times} = \{1,5,7,11,13,17,19,23\}$ is isomorphic to the additive group $(\mathbb{Z}/2\mathbb{Z})^3$. This fact plays a role in monstrous moonshine.
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Monstrous Moonshine
$\newcommand{\Q}{\mathbf Q} \newcommand{\Z}{\mathbf Z}$


I don't know about monstrous moonshine, but $(\Z/24\Z)^\times$ is the group of automorphisms of the maximal elementary abelian $2$-extension $\Q\_2\left(\root2\of{\Q\_2^\times}\right)=\Q\_2(\root2\of5, \root2\of3, \root2\of2)=\Q\_2(\zeta\_{24})$ of $\Q\_2$. See for example Lemma 8 of Lecture 19 of my [course](http://arxiv.org/abs/0903.2615)  on Local arithmetic.


