= Topological structure of a formal group on twice the 2-adic integers
{title2=$F(2\mathbb Z_2)\cong\mathbb Z_2\ \text{or}\ \mathbb Z/2\mathbb Z\times\mathbb Z_2$}
For a one-dimensional commutative integral <formal group law>, the <formal logarithm> identifies $F(4\mathbb Z_2)$ with $4\mathbb Z_2$. This is an index-two subgroup of $F(2\mathbb Z_2)$. Choose a topological generator $h$ of the subgroup and an element $v$ outside it, and write $2v=ch$. If $c$ is odd, $v$ generates the whole group. If $c$ is even, $v-(c/2)h$ has order two and splits off a cyclic factor. The <formal additive group> and <formal multiplicative group> realize the two cases.
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