| 仿射辛群作用下的面轨道生成的格 |
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| 引用本文： | 王兆飞,张贺,祝学理. 仿射辛群作用下的面轨道生成的格[J]. 数学的实践与认识, 2008, 38(23) |
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| 作者姓名： | 王兆飞 张贺 祝学理 |
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| 作者单位： | 河北北方学院新校区,数学系,河北,张家口,075000 |
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| 摘 要： | 设ASU(2v,F_q)是F_q上的2v维仿射辛空间,ASp_(2v)(F_q)是F_q上的2v次仿射辛群,设M(m,s)是ASp_(2v)(F_q)作用下的(m,s)面的轨道,用L(m,s)表示M(m,s)中面的交生成的集合.讨论了各轨道生成的集合之间的包含关系,一个面是由给定M(m,s)生成的集合中的一个元素的条件,以及L(m,s)何时做成几何格.
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| 关 键 词： | 仿射辛群 仿射辛空间 面的轨道 几何格 |
Lattices Generated by Orbits of Flats Under Finite Affine Symplectic Groups |
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| WANG Zhao-fei,ZHANG He,ZHU Xue-li. Lattices Generated by Orbits of Flats Under Finite Affine Symplectic Groups[J]. Mathematics in Practice and Theory, 2008, 38(23) |
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| Authors: | WANG Zhao-fei ZHANG He ZHU Xue-li |
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| Affiliation: | Department of Mathematics;Hebei North University;Zhangjiakou Hebei 075000;China |
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| Abstract: | Let ASG(2v,F_q)be the 2u-dimensional affine symplectic space over the finite field F_q,let ASp_(2v)(F_q)be the affine symplectic group of degree 2v over F_q,M(m,s)any orbit of(m,s) flats in under ASG(2v,F_q).Denote by L(m,s)the sets of flats which are intersections of flats in M(m,s),this paper discusses the relations of inclusion among sets generated by different orbits,a condition for which a flat is an element of set generated by the given orbit,and how the sets generated by orbits form the geometric lat... |
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| Keywords: | affine symplectic group affine symplectic space orbit of flats geometric lattices |
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