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On multiplication groups of relatively free quasigroups isotopic to Abelian groups
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 61-86
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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 $\mathop {\mathrm Mlt}Q$ is a Frobenius group. Conversely, if $\mathop {\mathrm Mlt}Q$ 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).
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 $\mathop {\mathrm Mlt}Q$ is a Frobenius group. Conversely, if $\mathop {\mathrm Mlt}Q$ 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).
Classification : 08B20, 20N05
Keywords: central quasigroups; $T$-quasigroups; multiplication groups; Frobenius groups; quasigroups isotopic to Abelian groups 
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Drápal, Aleš. On multiplication groups of relatively free quasigroups isotopic to Abelian groups. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 61-86. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a3/

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