| 群在集合上的广义作用及广义自同构群 |
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| 引用本文： | 谢芬芳,韦华全,马儇龙.群在集合上的广义作用及广义自同构群[J].广西师范学院学报(自然科学版),2012,29(2):17-20. |
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| 作者姓名： | 谢芬芳 韦华全 马儇龙 |
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| 作者单位： | 广西师范学院数学科学学院,广西南宁,530023 |
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| 基金项目： | 国家自然科学基金项目，广西自然科学基金项目，广西教育厅科研基会项目资助 |
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| 摘 要： | 设G1,G2是群,映射φ:G1→G2叫做G1到G2的广义同态映射,如果a,b∈G1,等式(ab)φ=aφbφ和(ab)φ=bφaφ,至少有一个成立.称群G广义作用在集合Ω上,如果群G到变换群SΩ有一个广义同态映射.通过研究有限群在集合上的广义作用及广义自同构群,得到了若干结果,推广了一些相关的经典定理.
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| 关 键 词： | 有限群 广义同态 广义作用 广义自同构群 |
Generalized Group Actions on Sets and Generalized Automorphis Groups |
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| XIE Fen-fang,WEI Hua-quan,MA Xuan-long.Generalized Group Actions on Sets and Generalized Automorphis Groups[J].Journal of Guangxi Teachers Education University:Natural Science Edition,2012,29(2):17-20. |
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| Authors: | XIE Fen-fang WEI Hua-quan MA Xuan-long |
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| Institution: | (School of Mathematical Sciences,Guangxi Teachers Education University,Nanning 530023,P.R.China) |
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| Abstract: | Given groups G1,G2.A mapping φ:G1→G2 is said to be a generalized homomor-phism from G1 to G2 if for any a,b in G,either(ab)α=aαbα or(ab)φ=bφaφ.A group G is said to be generalized acting on set Ω if there is a generalized homomorphism mapping from G to the trans-formation group SΩ.By studying the generalized acting of group on sets and generalized automorphism groups,we obtain some new results which generalize some related classical theorems. |
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| Keywords: | finite group generalized homomorphism generalized action generalized automorphism group |
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