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Wikipedia — Loop theory and quasigroup theory

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OP-9561AlgebraStatus unassessed

Existence of finite simple nonassociative automorphic loops

Can a finite simple automorphic loop fail to be associative?

Wikipedia — Loop theory and quasigroup theory· Wikipedia selection · status unassessed

OP-9560AlgebraStatus unassessed

Two-sided inverses in finite alternative loops

In every finite alternative loop, must each element's left and right inverses coincide?

Wikipedia — Loop theory and quasigroup theory· Wikipedia selection · status unassessed

OP-9559AlgebraStatus unassessed

Finiteness of finitely generated Moufang loops of exponent four or six

Must a finitely generated Moufang loop be finite if its exponent is four or six?

Wikipedia — Loop theory and quasigroup theory· Wikipedia selection · status unassessed

OP-9558AlgebraStatus unassessed

Restricted Burnside bounds for Moufang loops

Are orders of finite m -generated Moufang loops of exponent n bounded by a function of m,n alone?

Wikipedia — Loop theory and quasigroup theory· Wikipedia selection · status unassessed

OP-9557AlgebraStatus unassessed

Normality and nilpotency of Moufang Frattini subloops

In a finite Moufang loop, must the intersection of its maximal proper subloops be both normal and nilpotent?

Wikipedia — Loop theory and quasigroup theory· Wikipedia selection · status unassessed

OP-9556AlgebraStatus unassessed

Alternative-algebra embeddings of exponent-three commutative Moufang loops

Can every finite commutative Moufang loop of exponent three embed into a commutative alternative algebra?

Wikipedia — Loop theory and quasigroup theory· Wikipedia selection · status unassessed