This directory presents proofs about group theory, by Florian Kammüller. (Later, Larry Paulson simplified some of the proofs.) These theories use locales and were indeed the original motivation for locales. However, this treatment of groups must still be regarded as experimental. We can expect to see refinements in the future. Here is an outline of the directory's contents:
Group
defines
semigroups, groups, homomorphisms and the subgroup relation. It also defines
the product of two groups. It defines the factorization of a group and shows
that the factorization a normal subgroup is a group.
Bij
defines bijections over sets and operations on them and shows that they
are a group. It shows that automorphisms form a group.
Ring
defines rings and proves
a few basic theorems. Ring automorphisms are shown to form a group.
Sylow
contains a proof of the first Sylow theorem.
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