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Systems and their Generation
The Associative Law
22 other sections not shown
abelian group algebras Amer associator subloop autotopism Bruck C. R. Acad cancellation semigroup centrally nilpotent centre commutative Moufang loop completes the proof congruence coset defined demi-groupes denote descending chain conditions direct decompositions direct product elements of G endomorphism endomorphism of G equivalent exists free basis free loop G satisfies groupoid groupoid G halfgroupoid Hence homomorphism of G hypergroupes idempotent identity element identity mapping implies induces inner mapping integer inverse property isomorphic isotopic kernel left ideal Let G Let H loop G mapping of G minimal Moreover morphism multiplication necessary and sufficient non-empty set non-empty subset non-negative integer normal in G normal subloop operator loop G positive integer Proc projective plane proof of Lemma proof of Theorem proves pseudo-automorphism Q-projections Q-subloops quasigroup Russian Similarly simple semigroup skew-symmetric subgroup subhalfgroupoid subloop H subloop of G Theorem 2.1 theory unique zero