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1. On multiplication groups of relatively free quasigroups isotopic to Abelian groups

Creator:
Drápal, Aleš
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
central quasigroups, $T$-quasigroups, multiplication groups, Frobenius groups, and quasigroups isotopic to Abelian groups
Language:
English
Description:
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).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public