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:
Bij
defines bijections over sets and operations on them and shows that they
are a group.
DirProd
defines the product of two groups and proves that it is a group again.
FactGroup
defines the factorization of a group and shows that the factorization a
normal subgroup is a group.
Homomorphism
defines homomorphims and automorphisms for groups and rings and shows that
ring automorphisms are a group by using the previous result for
bijections.
Ring
and RingConstr
defines rings, proves a few basic theorems and constructs a lambda
function to extract the group that is part of the ring showing that it is
an abelian group.
Sylow
contains a proof of the first Sylow theorem.
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