360阶和504阶单群的唯一性的初等群论证明
An Elementary Proof for the Uniqueness (up to Isomorphism) of the Simple Groups of Order 360 and 504

作者: 周 峰 , 刘合国 :湖北大学数学系,武汉; 于浩然 , 王 杰 :北京大学数学系,北京;

关键词: Sylow定理单群PSL (29)PSL (28)Sylow’s Theorem Simple Group PSL (29) PSL (28)

摘要:
仅用Sylow定理、最基本的置换计算和线性代数重新证明了360阶单群同构于PSL(2,9)及504阶单群同构于PSL(2,8)。

Abstract: Only by using Sylow’s theorem, basic permutation computation and linear algebra theory, we prove that a simple group of order 360 is isomorphic to PSL(2,9) and a simple group of order 504 is isomorphic to PSL(2,8).

文章引用: 周 峰 , 于浩然 , 王 杰 , 刘合国 (2014) 360阶和504阶单群的唯一性的初等群论证明。 理论数学, 4, 172-178. doi: 10.12677/PM.2014.45026

参考文献

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[4] 周峰, 徐行忠, 廖军, 刘合国 (2014) 360阶单群同构于A6的初等群论证明. 理论数学, 1, 31-37.

[5] Cole, F.N. (1893) Simple groups as far as order 660. American Journal of Mathematics, 15, 303-315.

[6] 周峰, 徐涛, 刘合国 (2013) 660阶单群同构于PSL(2,11)的初等群论证明. 理论数学, 4, 241-243.

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