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Normality, nuclear squares and Osborn identities

Aleš Drápal, Michael Kinyon (2020)

Commentationes Mathematicae Universitatis Carolinae

Let $Q$ be a loop. If $S \leq Q$ is such that $ϕ (S) \subseteq S$ for each standard generator of Inn $Q$ , then $S$ does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that...

Not every Osborn loop is universal.

Jaiyéọlá, T.G., Adéníran, J.O. (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Note on analytic Moufang loops

Eugen Paal (2004)

Commentationes Mathematicae Universitatis Carolinae

It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.

Displaying 21 – 33 of 33

Normality, nuclear squares and Osborn identities

Not every Osborn loop is universal.

Note on analytic Moufang loops

Note on generalizing pregroups.

Note on isomorphism theorems of hyperrings.

Note on polyadic groups on sets with at most 7 elements

Notes on associative triples of elements in commutative groupoids

Notes on distributive groupoids

Notes on left distributive groupoids

Notes on quasimodules

Notes on the number of associative triples

Number of algebraic operations in idempotent groupoids

n-арные инверсные квазигруппы (J-квазигруппы)

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