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Start Over Subject Frobenius groups

1. A note on representing dowling geometries by partitions

Creator:
Matúš, František and Ben-Efraim, Aner
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
kybernetika, cybernetics, matroid representations, partition representations, Dowling geometries, Frobenius groups, 23, and 007
Language:
English
Description:
We prove that a rank ≥3 Dowling geometry of a group H is partition representable if and only if H is a Frobenius complement. This implies that Dowling group geometries are secret-sharing if and only if they are multilinearly representable., František Matúš and Aner Ben-Efraim., and Obsahuje bibliografické odkazy
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. 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