特征不为2的有限域上酉群的极小生成元集

高有;游宏

系统科学与数学 ›› 1999, Vol. 19 ›› Issue (1) : 46-050.

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PDF(213 KB)
系统科学与数学 ›› 1999, Vol. 19 ›› Issue (1) : 46-050. DOI: 10.12341/jssms09581
论文

特征不为2的有限域上酉群的极小生成元集

    高有,游宏
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SMALL SET OF GENERATORS OF UNITARY GROUPS OVER FINITE FIELDS OF CHARACTERISTIC NOT TWO

    You GAO,Hong YOU
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摘要

设K=Fq2为含有q2个元素的有限域,q为奇素数的幂,*:a→a*=aq是Fq2的一个二阶自同构.本文用几何方法证明了除K为F32而n=4的情形外,Fq2上的酉群Un(V)可由2个元素生成.

Abstract

Let K=F_(q~2) be a finite field with q~2 elements where q is a power of odd prime, and *: a->a~*=a~q be an automorphism of order 2 for all a implied by F_(q~2). In this paper, we show by geometric method that the unitary groups U_n(V) over F_(q~2) may be generated by two elements, except that K is F_(3~2) and n=4.

关键词

酉群 / 有限域 / 生成集

Key words

Finite field of characteristic not 2 / unitary groups / element of generators

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高有 , 游宏. 特征不为2的有限域上酉群的极小生成元集. 系统科学与数学, 1999, 19(1): 46-050. https://doi.org/10.12341/jssms09581
You GAO , Hong YOU. SMALL SET OF GENERATORS OF UNITARY GROUPS OVER FINITE FIELDS OF CHARACTERISTIC NOT TWO. Journal of Systems Science and Mathematical Sciences, 1999, 19(1): 46-050 https://doi.org/10.12341/jssms09581
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