Group
A group is defined by:
- Set of elements \(x\)
- An Operation \(*\)
- Closed under \(*\) (Unclosed is like division where \(5 / 3\) is not a natural)
- Identity \(e\): \(x * e = e * x\)
- Inverses \(x^{-1}\) exists: \(\forall{x}. x * x^{-1} = e\)
- Associativity \((a * b) * c = a * (b * c)\)
It is almost like a Monoid in Haskell
References
- Book: “Contemporary Abstract Algebra” by Gallian
- Videos: Socratica Abstract Algebra Playlist