| Maximal Subsemigroups of Finite Transformation Semigroups K（n, r） |
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| 作者姓名： | HaoBoYANG XiuLiangYANG |
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| 作者单位： | DepartmentofMathematics,HangzhouTeachersCollege,Hangzhou310036,P.R.China |
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| 摘 要： | Let Tn be the full transformation semigroup on the n-element set Xn. For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α∈Tn : |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of Tn.
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| 关 键 词： | 半群转化 有限 几何 最大子半群 零度半群 群论 |
| 收稿时间： | 17 September 2001 |
Maximal Subsemigroups of Finite Transformation Semigroups <Emphasis Type="Italic">K</Emphasis>(<Emphasis Type="Italic">n,r</Emphasis>) |
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| HaoBoYANG XiuLiangYANG.Maximal Subsemigroups of Finite Transformation Semigroups K(n,r)[J].Acta Mathematica Sinica,2004,20(3):475-482. |
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| Authors: | Hao Bo Yang Xiu Liang Yang |
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| Institution: | (1) Department of Mathematics, Hangzhou Teachers College, Hangzhou, 310036, P. R. China |
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| Abstract: | Abstract
Let T
n
be the full transformation semigroup on the n-element set X
n
. For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α ∈? T
n
: |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning
the number of subsemigroups of T
n
.
This work is supported by N. S. F. of Zhejiang Province and Hangzhou Teachers College |
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| Keywords: | Transformation semigroup Maximal subsemigroups |
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