Medial Quasigroups and Geometry.

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Medial Quasigroups and Geometry.

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Medial Quasigroups and Geometry.

Popis výsledku anglicky

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

Druh

B - Odborná kniha

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F05%2F2707" target="_blank" >GA201/05/2707: Riemannova a afinní geometrie podporovaná počítačem</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2006

Kód důvěrnosti údajů

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

ISBN

80-244-1399-X

Počet stran knihy

103

Název nakladatele

Univerzita Palackého

Místo vydání

Olomouc

Kód UT WoS knihy

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