前スレ421より
http://www-users.york.ac.uk/~bje1/galnotes.pdf
Symmetries of Equations: An Introduction to Galois Theory
Brent Everitt, version 1.12, December 19, 2007.

これで、12. Groups II: Symmetries of Fields ....69
(12.4) Symmetries of things normally arrange themselves into a group, and field symmetries are no
exception. We could talk just of the symmetry group of a field, but it turns out to be more instructive to
make a slightly more elaborate definition that takes into consideration not just fields, but their extensions:

とあります。
Symmetryと群
この理解が大事だな