6 Subgroups

Compare Subgroup.

It’s not clear if the author’s definition of “regular” is anything but a completely custom (and informal) description specific to the author. The author does provide a reference to a more technical definition in the footnote on pg. 98, however.

6.4 Cosets

Compare Coset.

See also, from Affine space:

Any coset of a subspace V of a vector space is an affine space over that subspace.

6.4 Lagrange’s theorem

Compare Lagrange’s theorem (group theory).