The structure of elements in finite full transformation semigroups
Gonca Ayık, Hayrullah Ayık, Yusuf Ünlü, John M Howie · Bulletin of the Australian Mathematical Society · 2005
Theindexandperiodof an elementaof a finite semigroup are the smallest values ofm≥ 1 andr≥ 1 such thatam+r= am. An element with indexmand period 1 is called anm-potentelement. For an element α of a finite full transformation semigroup with indexmand periodr, a unique factorisation α = σβ such that Shift(σ) ∩ Shift(β) = ∅ is obtained, where σ is a permutation of orderrand β is anm-potent. Some applications of this factorisation are given.