On products of all elements of a finite semigroup

PZ Hermann; Edmund Frederick Robertson; Nikola Ruskuc

doi:10.1017/S0013091500020514

On products of all elements of a finite semigroup

PZ Hermann, Edmund Frederick Robertson, Nikola Ruskuc

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

Abstract

Let S be a finite semigroup. Consider the set p(S) of all elements of S which can be represented as a product of all the elements of S in some order. It is shown that p(S) is contained in the minimal ideal M of S and intersects each maximal subgroup H of M in essentially the same way. The main result shows that p(S) intersects H in a union of cosets of H'.

Original language	English
Pages (from-to)	551-557
Number of pages	7
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	42
Issue number	3
DOIs	https://doi.org/10.1017/S0013091500020514
Publication status	Published - Oct 1999

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title = "On products of all elements of a finite semigroup",

abstract = "Let S be a finite semigroup. Consider the set p(S) of all elements of S which can be represented as a product of all the elements of S in some order. It is shown that p(S) is contained in the minimal ideal M of S and intersects each maximal subgroup H of M in essentially the same way. The main result shows that p(S) intersects H in a union of cosets of H'.",

author = "PZ Hermann and Robertson, \{Edmund Frederick\} and Nikola Ruskuc",

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AU - Hermann, PZ

AU - Robertson, Edmund Frederick

AU - Ruskuc, Nikola

PY - 1999/10

Y1 - 1999/10

N2 - Let S be a finite semigroup. Consider the set p(S) of all elements of S which can be represented as a product of all the elements of S in some order. It is shown that p(S) is contained in the minimal ideal M of S and intersects each maximal subgroup H of M in essentially the same way. The main result shows that p(S) intersects H in a union of cosets of H'.

AB - Let S be a finite semigroup. Consider the set p(S) of all elements of S which can be represented as a product of all the elements of S in some order. It is shown that p(S) is contained in the minimal ideal M of S and intersects each maximal subgroup H of M in essentially the same way. The main result shows that p(S) intersects H in a union of cosets of H'.

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U2 - 10.1017/S0013091500020514

DO - 10.1017/S0013091500020514

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VL - 42

SP - 551

EP - 557

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 3

ER -

On products of all elements of a finite semigroup

Abstract

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