Displaying similar documents to “On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops”

A class of commutative loops with metacyclic inner mapping groups

Aleš Drápal (2008)

Commentationes Mathematicae Universitatis Carolinae

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We investigate loops defined upon the product ℤ m × ℤ k by the formula ( a , i ) ( b , j ) = ( ( a + b ) / ( 1 + t f i ( 0 ) f j ( 0 ) ) , i + j ) , where f ( x ) = ( s x + 1 ) / ( t x + 1 ) , for appropriate parameters s , t ∈ ℤ m * . Each such loop is coupled to a 2-cocycle (in the group-theoretical sense) and this connection makes it possible to prove that the loop possesses a metacyclic inner mapping group. If s = 1 , then the loop is an A-loop. Questions of isotopism and isomorphism are considered in detail.

Sofic groups are not locally embeddable into finite Moufang loops

Heghine Ghumashyan, Jaroslav Guričan (2022)

Mathematica Bohemica

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We shall show that there exist sofic groups which are not locally embeddable into finite Moufang loops. These groups serve as counterexamples to a problem and two conjectures formulated in the paper by M. Vodička, P. Zlatoš (2019).

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

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A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

Schreier loops

Péter T. Nagy, Karl Strambach (2008)

Czechoslovak Mathematical Journal

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We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.