Simple quasigroups whose inner permutations commute

Tomáš Kepka; K. K. Ščukin

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A note on simple medial quasigroups

K. K. Ščukin (1993)

Commentationes Mathematicae Universitatis Carolinae

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A solvable primitive group with finitely generated abelian stabilizers is finite.

Quasigroups having at most three inner mappings

Tomáš Kepka (1989)

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On multiplication groups of relatively free quasigroups isotopic to Abelian groups

Aleš Drápal (2005)

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If $Q$ is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group $M l t Q$ is a Frobenius group. Conversely, if $M l t Q$ is a Frobenius group, $Q$ a quasigroup, then $Q$ has to be isotopic to an Abelian group. If $Q$ is, in addition, finite, then it must be a central quasigroup (a $T$ -quasigroup).