1
What is a group?
▶
1.1
Definition of a group
1.2
Examples
1.3
Cancellation, right inverse, right identity
1.4
Uniqueness and rearrangement
1.5
Inverses of inverses and of products
1.6
Natural-number powers
1.7
Order of an element
1.8
Permutations
1.9
Sign of a permutation
1.10
Dihedral groups
1.11
Abelian groups
1.12
Subgroups
1.13
Subgroups generated by a subset
1.14
Cyclic subgroups
1.15
Subgroups of \((\mathbb {Z}, +)\)
1.16
gcd and lcm
1.17
Group homomorphisms
1.18
Image, kernel, and the kernel test
1.19
Isomorphisms
1.20
Normal subgroups
1.21
The center
1.22
Centralizer, normalizer, and inner automorphisms
Dependency graph
Abstract Algebra in Lean
Louis (Yiyang) Liu
1
What is a group?
1.1
Definition of a group
1.2
Examples
1.3
Cancellation, right inverse, right identity
1.4
Uniqueness and rearrangement
1.5
Inverses of inverses and of products
1.6
Natural-number powers
1.7
Order of an element
1.8
Permutations
1.9
Sign of a permutation
1.10
Dihedral groups
1.11
Abelian groups
1.12
Subgroups
1.13
Subgroups generated by a subset
1.14
Cyclic subgroups
1.15
Subgroups of \((\mathbb {Z}, +)\)
1.16
gcd and lcm
1.17
Group homomorphisms
1.18
Image, kernel, and the kernel test
1.19
Isomorphisms
1.20
Normal subgroups
1.21
The center
1.22
Centralizer, normalizer, and inner automorphisms