About: Group structure and the axiom of choice

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In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellordered. In ZF set theory, i.e. ZFC without the axiom of choice, the following statements are equivalent: * For every nonempty set X there exists a binary operation • such that (X, •) is a group. * The axiom of choice is true.

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rdfs:label	Group structure and the axiom of choice (en)
rdfs:comment	In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellordered. In ZF set theory, i.e. ZFC without the axiom of choice, the following statements are equivalent: * For every nonempty set X there exists a binary operation • such that (X, •) is a group. * The axiom of choice is true. (en)
sameAs	Group structure and the axiom of choice
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Subject	Axiom of choice Group theory
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Link from a Wikipage to another Wikipage	Group (mathematics) Magma (algebra) Well-order Aleph Associative property Axiom of choice Bijection Binary operation Tarski's theorem about choice Cardinal number Cartesian product Axiom of choice Group theory Disjoint union Quasigroup Set (mathematics) Set theory Zermelo–Fraenkel set theory Cyclic group Dedekind-infinite set Complement (set theory) Ordinal number Empty set Equinumerosity Cantor–Bernstein theorem Monus Hartogs number Infimum and supremum Injective function Inner model Lexicographic order Mathematics
has abstract	In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellordered. In ZF set theory, i.e. ZFC without the axiom of choice, the following statements are equivalent: * For every nonempty set X there exists a binary operation • such that (X, •) is a group. * The axiom of choice is true. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Group_structure_and_the_axiom_of_choice
is Wikipage redirect of	Group Structure and the Axiom of Choice
is Link from a Wikipage to another Wikipage of	Group Structure and the Axiom of Choice Axiom of choice
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Group_structure_and_the_axiom_of_choice

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