cleanup for section on Groups

MIL/C08_Groups_and_Rings/C08_Groups_and_Rings.rst

@@ -3,15 +3,17 @@
 Groups and rings
 ================
 
-We saw in :numref:`proving_identities_in_algebraic_structures` how to prove and use lemmas about
-operations in groups and ring. Later in :numref:`section_algebraic_structures` we saw how
+We saw in :numref:`proving_identities_in_algebraic_structures` how to reason about
+operations in groups and rings. Later, in :numref:`section_algebraic_structures`, we saw how
 to define abstract algebraic structures, such as group structures, as well as concrete instances
-such as the ring structure on Gaussian integers. Then in Chapter :numref:`hierarchies`
-we saw how hierarchies of abstract structures are built.
+such as the ring structure on the Gaussian integers. :numref:`Chapter %s <hierarchies>` explained how
+hierarchies of abstract structures are handled in Mathlib.
 
-In this chapter we will explain a lot more about groups and rings in Mathlib. We won't be able to
-cover everything, especially since Mathlib constantly grows. But we will try to provide entry points
-and show how essential concepts appear. There is some overlap with the discussion of Chapter
-:numref:`hierarchies` but here we will emphasize how to use Mathlib instead of why Mathlib is
-built that way. If anything looks strange or convoluted then the explanation is probably
-in the previous chapter.
+In this chapter we work with groups and rings in more detail. We won't be able to
+cover every aspect of the treatement of these topics in Mathlib, especially since Mathlib is constantly growing.
+But we will provide entry points to the library and show how the essential concepts are used.
+There is some overlap with the discussion of
+:numref:`Chapter %s <hierarchies>`, but here we will focus on how to use Mathlib instead of the design
+decisions behind the way the topics are treated.
+So making sense of some of the examples may require reviewing the background from
+:numref:`Chapter %s <hierarchies>`.