Incoming links: Permutation
A concise to describe a specific permutation.
A permutation group can then be described in terms of the generating set of a group of specific elements given in cycle notation.
E.g. en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Permutation_groups mentions that the Mathieu group is generated by three elements:which feels quite compact for a simple group with 95040 elements, doesn't it!
- (0123456789a)
- (0b)(1a)(25)(37)(48)(69)
- (26a7)(3945)
Definition:
- odd permutation: -1
- even permutation: 1
- not a permutation: 0. This happens iff two more more indices are repeated
Group of all permutations.