Symmetric inverse semigroup
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In modern algebra, the set 
of all partial one-one transformations on a set X forms an inverse semigroup, called the symmetric inverse semigroup (or monoid) on X. In general is not commutative. More details are available in the discussion on the origins of the inverse semigroup.
[edit] Finite symmetric inverse semigroups
When X is a finite set {1, ..., n}, the inverse semigroup of one-one partial transformations is denoted by Cn and its elements are called charts[1]. The notion of chart generalizes the notion of permutation.
[edit] Notes
- ^ Lipscomb 1997, p. 1
[edit] References
S. Lipscomb, "Symmetric Inverse Semigroups", AMS Mathematical Surveys and Monographs (1997), ISBN 0821806270.
