| Simple groups with orders 2^a3^b5^cp^d, 2^a3^b7^cp^d and 2^a3^b5^c7^d |
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| 作者姓名： | JIANGYouyi TANMingshu LIUXuefei |
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| 作者单位： | [1]DepartmentofMathematics,ChongqingThreeGorgesCollege,Wanzhou404000,P.R.China [2]CollegeofMathematicsandPhysics,ChongqingUniversity,Chongqing40030,P.R.China |
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| 基金项目： | 重庆市自然科学基金
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重庆市自然科学基金 |
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| 摘 要： | This work deals with the power exponent r1 and r2 respectively of the maximal and second-maximal prime factors ofthe order of simple K4-group, and the classification for simple {5,7}′-K4-group G (i.e. ｜G｜ can not be divided by 5 nor by 7 or ｜π(G)｜ = 4 ), simple 5′ -K4-group G (i.e. ｜G｜ can not divided by 5 and ｜π(G)｜ =4) and simple 7′-Ea-group G (i.e. ｜G｜ can notdivided by 7 and ｜π(G)｜ =4). It is derived that r1 =1, 2 and 4, and r2 is not greater than 4. All the simple K4-groups with order 2^a3^b5^cp^d, 2^a3^b7^cp^d and 2^a3^b5^c7^d are obtained.
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| 关 键 词： | 有限群 简单K4群 分级理论 细致描述 能力指数丢番图方程 |
Simple groups with orders 2a3b5cpd,2a3b7cpd and 2a3b5c7d |
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| JIANGYouyi TANMingshu LIUXuefei.Simple groups with orders 2^a3^b5^cp^d, 2^a3^b7^cp^d and 2^a3^b5^c7^d[J].Journal of Chongqing University,2004,3(1):105-107. |
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| Authors: | JIANG Youyi TAN Mingshu Liu Xuefei |
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| Abstract: | This work deals with the power exponent r1 and r2 respectively of the maximal and second-maximal prime factors of the order of simple K4-group, and the classification for simple {5,7}'- K4-group G (i.e. |G| can not be divided by 5 nor by 7 or |π(G)| = 4 ), simple 5' - K4 -group G (i.e. |G| can not divided by 5 and |π(G)| =4) and simple 7'- K4 -group G (i.e. |G| can not divided by 7 and |π(G)| =4). It is derived that r1 =1, 2 and 4, and r2 is not greater than 4. All the simple K4 -groups with order 2a3b5cpd, 2a3b7cpd and 2a3b5c7d are obtained. |
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| Keywords: | finite grouo simple K44 -group classification theorem meticulous depiction power exponent Diophantine equation groups derived classification work power exponent maximal prime factors order simple |
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