On multiplication groups of relatively free quasigroups isotopic to Abelian groups

Aleš Drápal

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 1, page 61-86
  • ISSN: 0011-4642

Abstract

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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).

How to cite

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Drápal, Aleš. "On multiplication groups of relatively free quasigroups isotopic to Abelian groups." Czechoslovak Mathematical Journal 55.1 (2005): 61-86. <http://eudml.org/doc/30927>.

@article{Drápal2005,
abstract = {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 $\mathop \{\mathrm \{M\}lt\}Q$ is a Frobenius group. Conversely, if $\mathop \{\mathrm \{M\}lt\}Q$ 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).},
author = {Drápal, Aleš},
journal = {Czechoslovak Mathematical Journal},
keywords = {central quasigroups; $T$-quasigroups; multiplication groups; Frobenius groups; quasigroups isotopic to Abelian groups; central quasigroups; -quasigroups; multiplication groups; Frobenius groups; quasigroups isotopic to Abelian groups},
language = {eng},
number = {1},
pages = {61-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On multiplication groups of relatively free quasigroups isotopic to Abelian groups},
url = {http://eudml.org/doc/30927},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Drápal, Aleš
TI - On multiplication groups of relatively free quasigroups isotopic to Abelian groups
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 61
EP - 86
AB - 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 $\mathop {\mathrm {M}lt}Q$ is a Frobenius group. Conversely, if $\mathop {\mathrm {M}lt}Q$ 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).
LA - eng
KW - central quasigroups; $T$-quasigroups; multiplication groups; Frobenius groups; quasigroups isotopic to Abelian groups; central quasigroups; -quasigroups; multiplication groups; Frobenius groups; quasigroups isotopic to Abelian groups
UR - http://eudml.org/doc/30927
ER -

References

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