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- Finitely_generated_group abstract "In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the product of finitely many elements of the finite set S and of inverses of such elements.Every finite group is finitely generated, since S can be taken to be G itself. Every infinite finitely generated group must be countable but countable groups need not be finitely generated. The additive group of rational numbers Q is an example of a countable group that is not finitely generated.A group that is generated by a single element is called cyclic. Every infinite cyclic group is isomorphic to the additive group of the integers Z.".
- Finitely_generated_group thumbnail Dih4_cycle_graph.svg?width=300.
- Finitely_generated_group wikiPageID "963042".
- Finitely_generated_group wikiPageLength "4581".
- Finitely_generated_group wikiPageOutDegree "43".
- Finitely_generated_group wikiPageRevisionID "696652261".
- Finitely_generated_group wikiPageWikiLink Abelian_group.
- Finitely_generated_group wikiPageWikiLink Additive_group.
- Finitely_generated_group wikiPageWikiLink Algebra.
- Finitely_generated_group wikiPageWikiLink Algebraically_closed_group.
- Finitely_generated_group wikiPageWikiLink Ascending_chain_condition.
- Finitely_generated_group wikiPageWikiLink Category:Group_theory.
- Finitely_generated_group wikiPageWikiLink Category:Properties_of_groups.
- Finitely_generated_group wikiPageWikiLink Commutator_subgroup.
- Finitely_generated_group wikiPageWikiLink Countable_set.
- Finitely_generated_group wikiPageWikiLink Cyclic_group.
- Finitely_generated_group wikiPageWikiLink Decision_problem.
- Finitely_generated_group wikiPageWikiLink Direct_sum_of_groups.
- Finitely_generated_group wikiPageWikiLink Finite_group.
- Finitely_generated_group wikiPageWikiLink Finite_set.
- Finitely_generated_group wikiPageWikiLink Finitely_generated_abelian_group.
- Finitely_generated_group wikiPageWikiLink Finitely_generated_module.
- Finitely_generated_group wikiPageWikiLink Free_abelian_group.
- Finitely_generated_group wikiPageWikiLink Free_group.
- Finitely_generated_group wikiPageWikiLink Generating_set_of_a_group.
- Finitely_generated_group wikiPageWikiLink Group_(mathematics).
- Finitely_generated_group wikiPageWikiLink Group_isomorphism.
- Finitely_generated_group wikiPageWikiLink Index_of_a_subgroup.
- Finitely_generated_group wikiPageWikiLink Integer.
- Finitely_generated_group wikiPageWikiLink Inverse_element.
- Finitely_generated_group wikiPageWikiLink Lattice_of_subgroups.
- Finitely_generated_group wikiPageWikiLink Locally_cyclic_group.
- Finitely_generated_group wikiPageWikiLink Locally_finite_group.
- Finitely_generated_group wikiPageWikiLink Module_(mathematics).
- Finitely_generated_group wikiPageWikiLink Nielsen–Schreier_theorem.
- Finitely_generated_group wikiPageWikiLink Order_(group_theory).
- Finitely_generated_group wikiPageWikiLink Presentation_of_a_group.
- Finitely_generated_group wikiPageWikiLink Quotient_group.
- Finitely_generated_group wikiPageWikiLink Rank_of_an_abelian_group.
- Finitely_generated_group wikiPageWikiLink Rational_number.
- Finitely_generated_group wikiPageWikiLink Subgroup_series.
- Finitely_generated_group wikiPageWikiLink Torsion_group.
- Finitely_generated_group wikiPageWikiLink Word_(group_theory).
- Finitely_generated_group wikiPageWikiLink Word_problem_for_groups.
- Finitely_generated_group wikiPageWikiLink File:Cyclic_group.svg.
- Finitely_generated_group wikiPageWikiLink File:Dih4_cycle_graph.svg.
- Finitely_generated_group wikiPageWikiLinkText "Finitely generated group".
- Finitely_generated_group wikiPageWikiLinkText "Finitely generated".
- Finitely_generated_group wikiPageWikiLinkText "finitely generated group".
- Finitely_generated_group wikiPageWikiLinkText "finitely generated".
- Finitely_generated_group wikiPageUsesTemplate Template:Cite_book.
- Finitely_generated_group wikiPageUsesTemplate Template:Main.
- Finitely_generated_group wikiPageUsesTemplate Template:Reflist.
- Finitely_generated_group subject Category:Group_theory.
- Finitely_generated_group subject Category:Properties_of_groups.
- Finitely_generated_group hypernym G.
- Finitely_generated_group type Device.
- Finitely_generated_group type Redirect.
- Finitely_generated_group comment "In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the product of finitely many elements of the finite set S and of inverses of such elements.Every finite group is finitely generated, since S can be taken to be G itself. Every infinite finitely generated group must be countable but countable groups need not be finitely generated.".
- Finitely_generated_group label "Finitely generated group".
- Finitely_generated_group sameAs Q21083858.
- Finitely_generated_group sameAs Q21083858.
- Finitely_generated_group wasDerivedFrom Finitely_generated_group?oldid=696652261.
- Finitely_generated_group depiction Dih4_cycle_graph.svg.
- Finitely_generated_group isPrimaryTopicOf Finitely_generated_group.