半群PCS_n的极大子半群
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摘要
设C_n是X_n上的循环群,SP_n=P_n\S_n称为X_n上的部分奇异变换半群.通过对变换半群PCS_n=C_n∪SP_n的元素的分析,获得了变换半群PCS_n的极大子半群的完全分类.
Let C_n be the cyclic group on X_n, SP_n = P_n\S_n be the partial singular transformation semigroup on X_n. By analyzing the elements of the transformation semigroup PCS_n =C_n∪SP_n, the classification of the maximal subsemigroup of the transformation semigroup PCS_n is obtained.
Let C_n be the cyclic group on X_n, SP_n = P_n\S_n be the partial singular transformation semigroup on X_n. By analyzing the elements of the transformation semigroup PCS_n =C_n∪SP_n, the classification of the maximal subsemigroup of the transformation semigroup PCS_n is obtained.
引文
[1] GANYUSHKIN O, MAZORCHUK V. Classical Finite Transformation Semigroups[M]. London:Springer-Verlag, 2009.
[2] HOWIE J M,McFadden R B. Idempotent Rank in Finite Pull Transformation Semigroups[J].Proceedings of the Royal Society of Edinburgh, 1990, 114(3-4):161-167.
[3] Xiuliang Yang. Maximal subsemigroups of the finite singular transformation semigroup[J]. comm in Algebra, 2001, 39(3):1175-1182.
[4] Xiuliang Yang. A classification of the maximal inverse subsemigroups of finite symmetric inverse semigroups[J]. comm in Algebra, 1999, 27(8):4089-4096.
[5]徐波.保序压缩变换半群的极大子半群[J].贵州师范大学学报:自然科学版,2012, 30(4):63-65.
[6]罗永贵.半群W(n,r)的极大(正则)子半群[J].山东大学学报:理学版,2017, 52(10):7-11.
[7]罗永贵.半群W(n,r)的非群元秩和相关秩[J].山东大学学报:理学版,2013, 48(12):70-74.
[8]罗永贵.半群L_D(n,r)的极大正则子半群[J].西南师范大学学报:自然科学版,2017, 42(8):32-37.
[9]张钱,赵平.半群CS_n的秩[J].数学的实践与认识,2018,48(11):241-246.
[10] HOWIE J M. Fundamentals of Semigroup Theory[M]. Oxford:Oxford University Press,1995.
[11]孙宗明.群的极大子群与群的构造[J].高师理科学刊,1985(01):13-17.
[12] Reyadhr Khazal. A note on maximal subgroups in finite group[J]. Proceedings of'GROUPSKOREA 1988'pusan, august, 1988:106-109.
[2] HOWIE J M,McFadden R B. Idempotent Rank in Finite Pull Transformation Semigroups[J].Proceedings of the Royal Society of Edinburgh, 1990, 114(3-4):161-167.
[3] Xiuliang Yang. Maximal subsemigroups of the finite singular transformation semigroup[J]. comm in Algebra, 2001, 39(3):1175-1182.
[4] Xiuliang Yang. A classification of the maximal inverse subsemigroups of finite symmetric inverse semigroups[J]. comm in Algebra, 1999, 27(8):4089-4096.
[5]徐波.保序压缩变换半群的极大子半群[J].贵州师范大学学报:自然科学版,2012, 30(4):63-65.
[6]罗永贵.半群W(n,r)的极大(正则)子半群[J].山东大学学报:理学版,2017, 52(10):7-11.
[7]罗永贵.半群W(n,r)的非群元秩和相关秩[J].山东大学学报:理学版,2013, 48(12):70-74.
[8]罗永贵.半群L_D(n,r)的极大正则子半群[J].西南师范大学学报:自然科学版,2017, 42(8):32-37.
[9]张钱,赵平.半群CS_n的秩[J].数学的实践与认识,2018,48(11):241-246.
[10] HOWIE J M. Fundamentals of Semigroup Theory[M]. Oxford:Oxford University Press,1995.
[11]孙宗明.群的极大子群与群的构造[J].高师理科学刊,1985(01):13-17.
[12] Reyadhr Khazal. A note on maximal subgroups in finite group[J]. Proceedings of'GROUPSKOREA 1988'pusan, august, 1988:106-109.