设N, H是任意的群. 若存在群G,它具有正规子群Ñ ≤ Z(G),使得Ñ ≌ N且G/Ñ ≌ H, 则称群G为N被H的中心扩张.本文完全分类了当N为p3阶初等交换p群及H为内交换p群时, N被H的中心扩张得到的所有不同构的群. 从而我们完全分类了初等交换p群被内交换p群的中心扩张得到的所有不同构的群.
Abstract
Assume N and H are groups. If there is a group G which has a normal subgroup Ñ ≤ Z(G) such that Ñ ≌ N and G/Ñ ≌ H, then G is called a central extension of N by H. In this paper, we classified all groups which are central extensions of N by H, where N is an elementary abelian p-group of order p3 and H is an inner abelian p-group. Thus all groups which are central extensions of an elementary abelian p-group by an inner abelian p-group are classified.
关键词
中心扩张 /
初等交换p群 /
内交换p群
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Key words
central extension /
elementary abelian p-groups /
inner abelian p-groups
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参考文献
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脚注
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基金
国家自然科学基金资助项目(11071150);山西省自然科学基金(2008012001)和山西省回国留学人员科研项目([2007]13-56)
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