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- Elementary_abelian_group abstract "In group theory, an elementary abelian group (or elementary abelian p-group) is an abelian group in which every nontrivial element has order p. The number p must be prime, and the elementary abelian groups are a particular kind of p-group. The case where p = 2, i.e., an elementary abelian 2-group, is sometimes called a Boolean group.Every elementary abelian p-group is a vector space over the prime field with p elements, and conversely every such vector space is an elementary abelian group.By the classification of finitely generated abelian groups, or by the fact that every vector space has a basis, every finite elementary abelian group must be of the form (Z/pZ)n for n a non-negative integer (sometimes called the group's rank). Here, Z/pZ denotes the cyclic group of order p (or equivalently the integers mod p), and the superscript notation means the n-fold direct product of groups.In general, a (possibly infinite) elementary abelian p-group is a direct sum of cyclic groups of order p. (Note that in the finite case the direct product and direct sum coincide, but this is not so in the infinite case.)Presently, in the rest of this article, these groups are assumed finite.".
- Elementary_abelian_group wikiPageID "4843202".
- Elementary_abelian_group wikiPageLength "6787".
- Elementary_abelian_group wikiPageOutDegree "28".
- Elementary_abelian_group wikiPageRevisionID "679903965".
- Elementary_abelian_group wikiPageWikiLink Abelian_group.
- Elementary_abelian_group wikiPageWikiLink Automorphism.
- Elementary_abelian_group wikiPageWikiLink Category:Abelian_group_theory.
- Elementary_abelian_group wikiPageWikiLink Category:Finite_groups.
- Elementary_abelian_group wikiPageWikiLink Category:P-groups.
- Elementary_abelian_group wikiPageWikiLink Characteristic_(algebra).
- Elementary_abelian_group wikiPageWikiLink Classification_of_finitely_generated_abelian_groups.
- Elementary_abelian_group wikiPageWikiLink Cyclic_group.
- Elementary_abelian_group wikiPageWikiLink Direct_product_of_groups.
- Elementary_abelian_group wikiPageWikiLink Direct_sum.
- Elementary_abelian_group wikiPageWikiLink Elementary_group.
- Elementary_abelian_group wikiPageWikiLink Endomorphism.
- Elementary_abelian_group wikiPageWikiLink Extra_special_group.
- Elementary_abelian_group wikiPageWikiLink Finite_field.
- Elementary_abelian_group wikiPageWikiLink Finite_group.
- Elementary_abelian_group wikiPageWikiLink Finitely_generated_abelian_group.
- Elementary_abelian_group wikiPageWikiLink General_linear_group.
- Elementary_abelian_group wikiPageWikiLink Group_theory.
- Elementary_abelian_group wikiPageWikiLink Hamming_space.
- Elementary_abelian_group wikiPageWikiLink Heisenberg_group.
- Elementary_abelian_group wikiPageWikiLink Klein_four-group.
- Elementary_abelian_group wikiPageWikiLink Linear_algebra.
- Elementary_abelian_group wikiPageWikiLink Modular_arithmetic.
- Elementary_abelian_group wikiPageWikiLink Module_(mathematics).
- Elementary_abelian_group wikiPageWikiLink P-group.
- Elementary_abelian_group wikiPageWikiLink Presentation_of_a_group.
- Elementary_abelian_group wikiPageWikiLink Prime_field.
- Elementary_abelian_group wikiPageWikiLink Symmetric_difference.
- Elementary_abelian_group wikiPageWikiLink Vector_space.
- Elementary_abelian_group wikiPageWikiLinkText "Elementary abelian 2-group".
- Elementary_abelian_group wikiPageWikiLinkText "Elementary abelian group".
- Elementary_abelian_group wikiPageWikiLinkText "Elementary".
- Elementary_abelian_group wikiPageWikiLinkText "elementary ''p''-groups".
- Elementary_abelian_group wikiPageWikiLinkText "elementary abelian 2-group".
- Elementary_abelian_group wikiPageWikiLinkText "elementary abelian 2-groups".
- Elementary_abelian_group wikiPageWikiLinkText "elementary abelian group".
- Elementary_abelian_group wikiPageWikiLinkText "elementary abelian subgroup".
- Elementary_abelian_group wikiPageWikiLinkText "elementary abelian".
- Elementary_abelian_group date "April 2015".
- Elementary_abelian_group hasPhotoCollection Elementary_abelian_group.
- Elementary_abelian_group reason "do not assume finite unless stated".
- Elementary_abelian_group wikiPageUsesTemplate Template:=.
- Elementary_abelian_group wikiPageUsesTemplate Template:Cleanup.
- Elementary_abelian_group subject Category:Abelian_group_theory.
- Elementary_abelian_group subject Category:Finite_groups.
- Elementary_abelian_group subject Category:P-groups.
- Elementary_abelian_group hypernym Group.
- Elementary_abelian_group type Band.
- Elementary_abelian_group type Group.
- Elementary_abelian_group type Group.
- Elementary_abelian_group comment "In group theory, an elementary abelian group (or elementary abelian p-group) is an abelian group in which every nontrivial element has order p. The number p must be prime, and the elementary abelian groups are a particular kind of p-group.".
- Elementary_abelian_group label "Elementary abelian group".
- Elementary_abelian_group sameAs زمرة_أبيلية_ابتدائية.
- Elementary_abelian_group sameAs Elementaarinen_Abelin_ryhmä.
- Elementary_abelian_group sameAs Gruppo_abeliano_elementare.
- Elementary_abelian_group sameAs m.0cqk5n.
- Elementary_abelian_group sameAs Q1017231.
- Elementary_abelian_group sameAs Q1017231.
- Elementary_abelian_group sameAs 初等阿貝爾群.
- Elementary_abelian_group wasDerivedFrom Elementary_abelian_group?oldid=679903965.
- Elementary_abelian_group isPrimaryTopicOf Elementary_abelian_group.