6 · Compare divisible groups

A divisible group allows division by every positive integer. The additive real numbers have this property, but the integers do not.

Try this. Choose a group and increase the number of divisions. Watch for the first result that leaves the group. The final line explains why every map from a divisible group to an integer coordinate is zero.

This arithmetic explains an obstruction to mapping the reals into the projective building blocks of solid groups. Corollary 6.1 (iii), using Theorem 4.3, proves the stronger derived vanishing result.