Medial Quasigroups and Geometry.

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F06%3A00009825" target="_blank" >RIV/61989592:15310/06:00009825 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Medial Quasigroups and Geometry.

Original language description

The relationship of medial quasigroups to commutative groups, nearfields, and affine geometry are explained, particularly in the finite case. Comparing various view-points and methods, the following topics are discussed: How to derive medial quasigroupsfrom abelian groups (Toyoda's theorem). The relatioship of loops to web geometry. How particular quasigroups - of type (n,k) - are related to affine spaces or affine desarquesian planes (Pucharev's Theorem). How homogeneous quasigroups are related to nearfields. How special classes of medial quasigroups (e.g. the so-called golden section quasigroups) generate parallelogram spaces and various interesting geometric configurations such as parallelograms and trapezoids. Results reached by various authors (R.H. Bruck, N.K. Pucharev, S.K. Stein, J. Šiftar, J. Duplák, V. Volenec, Z.Begovič-Kolář, Krčadinac, Bombardelli etc.) are presented in a unified language and notation, and supplied or completed by perceptions, observations, remarks and v

Czech name

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Czech description

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Type

B - Specialist book

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F05%2F2707" target="_blank" >GA201/05/2707: Computer-assisted research in Riemannian and affine geometry</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2006

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

80-244-1399-X

Number of pages

103

Publisher name

Univerzita Palackého

Place of publication

Olomouc

UT code for WoS book

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