Matches in DBpedia 2016-04 for { ?s ?p "In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st = suu−1t, but s ≠ t−1 for s,t,u∈S). The members of S are called generators of FS.An arbitrary group G is called free if it is isomorphic to FS for some subset S of G, that is, if there is a subset S of G such that every element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st = suu−1t).A related but different notion is a free abelian group, both notions are particular instances of a free object from universal algebra."@en }
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- Free_group abstract "In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st = suu−1t, but s ≠ t−1 for s,t,u∈S). The members of S are called generators of FS.An arbitrary group G is called free if it is isomorphic to FS for some subset S of G, that is, if there is a subset S of G such that every element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st = suu−1t).A related but different notion is a free abelian group, both notions are particular instances of a free object from universal algebra.".
- Q431078 abstract "In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st = suu−1t, but s ≠ t−1 for s,t,u∈S). The members of S are called generators of FS.An arbitrary group G is called free if it is isomorphic to FS for some subset S of G, that is, if there is a subset S of G such that every element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st = suu−1t).A related but different notion is a free abelian group, both notions are particular instances of a free object from universal algebra.".