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Un gruppo è un insieme munito di un'operaz … Un gruppo è un insieme munito di un'operazione associativa dotata di elemento neutro e tale che ogni elemento possiede un inverso. Gruppi molto importanti sono costituiti da trasformazioni; altri gruppi che si incontrano spesso sono costituiti da insiemi numerici muniti della moltiplicazione. In genere l'operazione di un gruppo viene chiamata prodotto e il suo elemento neutro viene detto unità o elemento identità. In questo articolo useremo e per denotare l'unità di un gruppo.eremo e per denotare l'unità di un gruppo.
, 群 (G, •) は集合 G で三つの公理を満たす G 上の（つまり G において閉 … 群 (G, •) は集合 G で三つの公理を満たす G 上の（つまり G において閉じた）二項演算 "•" を組にしたものである。群の三公理とは
* 演算の結合律: G の任意の元 a, b, c に対して (a • b) • c = a • (b • c) が成り立つ。
* 単位元の存在: e ∈ G が存在して、G のいかなる元 a に対しても e • a = a • e = a を満たす。
* 逆元の存在: G のそれぞれの元 a に対して a • b = b • a = e を満たす G の元 b が存在する。ここで e は単位元。 群の簡単な例としては整数全体の集合 Z に加法を考えたもの、0 でない有理数全体の成す集合 Q× に乗法を考えたものが挙げられる。後者はもっと一般に任意の 環 R について、その単元の全体 R× は乗法群を成す。群の定義および更なる例については群の項に譲る。しかし群には上に挙げたものよりももっと一般の構造が含まれる。群論とは、問題とする群の演算や元が具体的にどのような姿をしているかということに依存しない、群についての抽象的な言明を与えることを目的とするものである。 この用語集では群論において広く用いられる基本的な概念についての短い説明を提供する。群論の話題についての一般の記述は群論の項を参照されたい。また、群論の話題一覧 等も参照のこと。についての一般の記述は群論の項を参照されたい。また、群論の話題一覧 等も参照のこと。
, Для загального ознайомлення з теорією груп див. Група (математика) і Теорія груп. Курсив позначає посилання на цей словник.
, In mathematics and abstract algebra, group … In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.s also central to public key cryptography.
, В этой статье приведены основные термины, используемые в теории групп. Курсив обозначает внутреннюю ссылку на данный глоссарий. В конце приводится таблица основных обозначений, применяемых в теории групп.
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, http://uk.dbpedia.org/resource/%D0%A1%D0%BB%D0%BE%D0%B2%D0%BD%D0%B8%D0%BA_%D1%82%D0%B5%D1%80%D0%BC%D1%96%D0%BD%D1%96%D0%B2_%D1%82%D0%B5%D0%BE%D1%80%D1%96%D1%97_%D0%B3%D1%80%D1%83%D0%BF +
, http://ru.dbpedia.org/resource/%D0%93%D0%BB%D0%BE%D1%81%D1%81%D0%B0%D1%80%D0%B8%D0%B9_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B8_%D0%B3%D1%80%D1%83%D0%BF%D0%BF +
, http://it.dbpedia.org/resource/Glossario_di_teoria_dei_gruppi +
, http://id.dbpedia.org/resource/Daftar_topik_teori_grup +
, http://fr.dbpedia.org/resource/Lexique_des_groupes +
, http://tr.dbpedia.org/resource/Grup_teorisinin_konular%C4%B1n%C4%B1n_listesi +
, http://dbpedia.org/resource/List_of_group_theory_topics +
, http://ar.dbpedia.org/resource/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D9%85%D9%88%D8%A7%D8%B6%D9%8A%D8%B9_%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%B2%D9%85%D8%B1 +
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Un gruppo è un insieme munito di un'operaz … Un gruppo è un insieme munito di un'operazione associativa dotata di elemento neutro e tale che ogni elemento possiede un inverso. Gruppi molto importanti sono costituiti da trasformazioni; altri gruppi che si incontrano spesso sono costituiti da insiemi numerici muniti della moltiplicazione. In genere l'operazione di un gruppo viene chiamata prodotto e il suo elemento neutro viene detto unità o elemento identità. In questo articolo useremo e per denotare l'unità di un gruppo.eremo e per denotare l'unità di un gruppo.
, 群 (G, •) は集合 G で三つの公理を満たす G 上の（つまり G において閉 … 群 (G, •) は集合 G で三つの公理を満たす G 上の（つまり G において閉じた）二項演算 "•" を組にしたものである。群の三公理とは
* 演算の結合律: G の任意の元 a, b, c に対して (a • b) • c = a • (b • c) が成り立つ。
* 単位元の存在: e ∈ G が存在して、G のいかなる元 a に対しても e • a = a • e = a を満たす。
* 逆元の存在: G のそれぞれの元 a に対して a • b = b • a = e を満たす G の元 b が存在する。ここで e は単位元。 群の簡単な例としては整数全体の集合 Z に加法を考えたもの、0 でない有理数全体の成す集合 Q× に乗法を考えたものが挙げられる。後者はもっと一般に任意の 環 R について、その単元の全体 R× は乗法群を成す。群の定義および更なる例については群の項に譲る。しかし群には上に挙げたものよりももっと一般の構造が含まれる。群論とは、問題とする群の演算や元が具体的にどのような姿をしているかということに依存しない、群についての抽象的な言明を与えることを目的とするものである。 この用語集では群論において広く用いられる基本的な概念についての短い説明を提供する。群論の話題についての一般の記述は群論の項を参照されたい。また、群論の話題一覧 等も参照のこと。についての一般の記述は群論の項を参照されたい。また、群論の話題一覧 等も参照のこと。
, В этой статье приведены основные термины, используемые в теории групп. Курсив обозначает внутреннюю ссылку на данный глоссарий. В конце приводится таблица основных обозначений, применяемых в теории групп.
, In mathematics and abstract algebra, group … In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.e become subject areas in their own right.
, Для загального ознайомлення з теорією груп див. Група (математика) і Теорія груп. Курсив позначає посилання на цей словник.
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群論の用語
, Глоссарий теории групп
, Daftar topik teori grup
, List of group theory topics
, قائمة مواضيع نظرية الزمر
, Словник термінів теорії груп
, Lexique des groupes
, Glossario di teoria dei gruppi
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http://dbpedia.org/resource/List_of_representation_theory_topics +
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