7 · Read a completed tensor product

The completed tensor product combines two solid groups and keeps completion directions that are compatible with both sides.

Try this. Choose p-adic groups for two different primes and observe the zero result. Then compare equal prime directions and power-series directions, which remain in the answer.

Example 6.4 states five identities. Proposition 6.3 explains the power-series example by pairing coordinate sets. The readout distinguishes quoted identities from entries obtained by relabelling that rule.