Quasigroups and Loops: Introduction |
Contents
Quasigroups and loops | 1 |
Quasigroups and geometry | 34 |
Isotopy theory for quasigroups | 57 |
Copyright | |
3 other sections not shown
Common terms and phrases
abelian group automorphism autotopism of Q bijection binary operation Bol loop Bruck called carrier set Cayley table commutative Moufang loop Complete the proof Corollary decomposition modulo defined Definition denote di-associative distributive quasigroup element for G entropic quasigroup equivalence relation Example Exercise f,g-isotope g-isotope G-loop groupoid G I.P. loop idempotent identical relation identity element implies isomorphic isotopic invariant isotopism of G Lemma Let G Let Q loop G loop with identity loop-isotope loops of order modulo H Moufang identity N₁ N₁(G nilpotency normal subgroup normal subloop normal subquasigroup nucleus operation table permutations planar ternary ring principal isotope proof of Theorem prove pseudo-automorphism with companion quasigroups and loops right companion right pseudo-automorphism satisfies Section set G Steiner triple systems subloop of G subset T.S. quasigroup Theorem totally symmetric quasigroup unique W.I.P. loop