翻訳と辞書 Words near each other ・ Central Presbyterian Church (New York City) ・ Central Presbyterian Church (Saint Paul, Minnesota) ・ Central Presbyterian Church (Waxahachie, Texas) ・ Central Press ・ Central Press Association ・ Central Prison ・ Central Prison Haripur ・ Central Prison Karachi ・ Central Prison Peshawar ・ Central Prison, Kannur ・ Central Prison, Poojappura ・ Central Prison, Viyyur ・ Central Private School (Central, Louisiana) ・ Central processing unit ・ Central processing unit (musician) ・ Central product ・ Central Product Classification ・ Central Professional Hockey League ・ Central Provident Fund ・ Central Province ・ Central Province (Kenya) ・ Central Province (Papua New Guinea) ・ Central Province (Solomon Islands) ・ Central Province (Sri Lanka) bus routes ・ Central Province (Victoria) ・ Central Province Rugby Football Union ・ Central Province, Maldives ・ Central Province, Sri Lanka ・ Central Province, Zambia ・ Central Provinces Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Central product ： ウィキペディア英語版 Central product In mathematics, especially in the field of group theory, the central product is way of producing a group from two smaller groups. The central product is similar to the direct product, but in the central product two isomorphic central subgroups of the smaller groups are merged into a single central subgroup of the product. Central products are an important construction and can be used for instance to classify extraspecial groups. ==Definition== There are several related but distinct notions of central product. Similarly to the direct product, there are both internal and external characterizations, and additionally there are variations on how strictly the intersection of the factors is controlled. A group ''G'' is an internal central product of two subgroups ''H'', ''K'' if (1) ''G'' is generated by ''H'' and ''K'' and (2) every element of ''H'' commutes with every element of ''K'' . Sometimes the stricter requirement that ''H'' ∩ ''K'' is exactly equal to the center is imposed, as in . The external central product is constructed from two groups ''H'' and ''K'', two subgroups ''H''1 ≤ Z(''H''), ''K''1 ≤ Z(''K''), and a group isomorphism ''θ'':''H''1 → ''K''1. The external central product is the quotient of the direct product ''H'' × ''K'' by the normal subgroup ''N'' = , . Sometimes the stricter requirement that ''H''1 = Z(''H'') and ''K''1 = Z(''K'') is imposed, as in . An internal central product is isomorphic to an external central product with ''H''1 = ''K''1 = ''H'' ∩ ''K'' and ''θ'' the identity. An external central product is an internal central product of the images of ''H'' × 1 and 1 × ''K'' in the quotient group ( ''H'' × ''K'' ) / ''N''. This is shown for each definition in and . Note that the external central product is not in general determined by its factors ''H'' and ''K'' alone. The isomorphism type of the central product will depend on the isomorphism ''θ''. It is however well defined in some notable situations, for example when ''H'' and ''K'' are both finite extra special groups and ''H''1 = Z(''H'') and ''K''1 = Z(''K''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Central product」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.