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- Glossary_of_group_theory abstract "In group theory, a group (G, •) is a set G closed under a binary operation • satisfying the following 3 axioms: Associativity: For all a, b and c in G, (a • b) • c = a • (b • c). Identity element: There exists an e∈G such that for all a in G, e • a = a • e = a. Inverse element: For each a in G, there is an element b in G such that a • b = b • a = e, where e is an identity element.Basic examples for groups are the integers Z with addition operation, or rational numbers without zero Q\{0} with multiplication. More generally, for any ring R, the units in R form a multiplicative group. See the group article for an illustration of this definition and for further examples. Groups include, however, much more general structures than the above. Group theory is concerned with proving abstract statements about groups, regardless of the actual nature of element and the operation of the groups in question. This glossary provides short explanations of some basic notions used throughout group theory. Please refer to group theory for a general description of the topic. See also list of group theory topics.".
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- Glossary_of_group_theory subject Category:Glossaries_of_mathematics.
- Glossary_of_group_theory subject Category:Group_theory.
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- Glossary_of_group_theory comment "In group theory, a group (G, •) is a set G closed under a binary operation • satisfying the following 3 axioms: Associativity: For all a, b and c in G, (a • b) • c = a • (b • c). Identity element: There exists an e∈G such that for all a in G, e • a = a • e = a.".
- Glossary_of_group_theory label "Glossario di teoria dei gruppi".
- Glossary_of_group_theory label "Glossary of group theory".
- Glossary_of_group_theory label "Lexique des groupes".
- Glossary_of_group_theory label "Глоссарий теории групп".
- Glossary_of_group_theory label "لائحة المواضيع المتعلقة بنظرية الزمر".
- Glossary_of_group_theory label "群論の用語".
- Glossary_of_group_theory sameAs Lexique_des_groupes.
- Glossary_of_group_theory sameAs Glossario_di_teoria_dei_gruppi.
- Glossary_of_group_theory sameAs 群論の用語.
- Glossary_of_group_theory sameAs Q1052627.
- Glossary_of_group_theory sameAs Q1052627.
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