The structure of elements in finite full transformation semigroups

G Ayik, H Ayik, Y Unlu, J M Howie

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

The index and period of an element a of a finite semigroup are the smallest values of m >= 1 and r >= 1 such that a(m+r) = a(m). An element with index m and period 1 is called an m-potent element. For an element a of a finite full transformation semigroup with index m and period r, a unique factorisation alpha = sigma beta such that Shift(sigma) boolean AND Shift(beta) = theta is obtained, where sigma is a permutation of order r and beta is an m-potent. Some applications of this factorisation are given.

Original languageEnglish
Pages (from-to)69-74
Number of pages6
JournalBulletin of the Australian Mathematical Society
Volume71
Publication statusPublished - Feb 2005

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