The structure of elements in finite full transformation semigroups

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

The structure of elements in finite full transformation semigroups

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

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	69-74
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	71
Publication status	Published - Feb 2005

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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.",

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AU - Unlu, Y

AU - Howie, J M

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N2 - 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.

AB - 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.

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VL - 71

SP - 69

EP - 74

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

ER -

The structure of elements in finite full transformation semigroups

Abstract

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