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有限可換群の、部分群の個数を求める計算法
https://doi.org/10.34356/00000068
https://doi.org/10.34356/00000068775f6437-227a-4290-8fb1-11faf8b9e743
名前 / ファイル | ライセンス | アクション |
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有限可換群の、部分群の個数を求める計算法 (58.9 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2010-12-07 | |||||
タイトル | ||||||
タイトル | 有限可換群の、部分群の個数を求める計算法 | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
ID登録 | ||||||
ID登録 | 10.34356/00000068 | |||||
ID登録タイプ | JaLC | |||||
別タイトル | ||||||
その他のタイトル | Formula of the Number of Subgroups of a Finite Abelian Group | |||||
著者 |
清田, 秀憲
× 清田, 秀憲 |
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著者別名 | ||||||
姓名 | KIYOTA, Hidenori | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | A finite Abelian group is decomposed into a direct product of subgroups of prime-power orders.These subgroups are commutative p-groups,known p-Sylow groups.Every commutative p-group S is decomposed into a direct product of cyclic subgroups C(pk1)×C(pk2)×…C(pkt), by an abbreviated notation(k1, k2, …,kt). Let H be a type(h1, h2, …, hs)subgroup of S . First, we make bases(a1, a2, …,as)such that a'i s(i= 1 … s)are elements of S of order phi. Then we prove that there are (pf(h1)-pf(h1-1))(pf(h2)-pf(h2-1)+1)…(pf(hs)-pf(hs-1)+s-1) basis. Similarly, there are (pg(h1)-pg(h1-1))(pg(h2)-pg(h2-1)+1)…(pg(hs)-pg(hs-1)+s-1) basis of H. We prove that the number of type(h1, h2, …, hs)subgroups of S is Πsi=1(pf(hi)-pf(hi-1)+i-1) ───────────── . Πsi=1(pg(hi)-pg(hi-1)+i-1) Then we have a theorem to compute those of a finite Abelian group. | |||||
出版者 | ||||||
出版者 | 都留文科大学 | |||||
書誌情報 |
都留文科大学研究紀要 en : 都留文科大学研究紀要 号 51, p. 83-90, 発行日 1999-10-20 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0286-3774 | |||||
NCID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00149431 | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |