The centre of a Steiner loop and the maxi-Pasch problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438471" target="_blank" >RIV/00216208:11320/21:10438471 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YPk4ffP9Pz" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YPk4ffP9Pz</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2020.035" target="_blank" >10.14712/1213-7243.2020.035</a>

Result language
angličtina
Original language name
The centre of a Steiner loop and the maxi-Pasch problem
Original language description
A binary operation "." which satisfies the identities x . e = x, x . x = e, (x . y) . x = y and x . y = y . x is called a Steiner loop. This paper revisits the proof of the necessary and sufficient conditions for the existence of a Steiner loop of order n with centre of order m and discusses the connection of this problem to the question of the maximum number of Pasch configurations which can occur in a Steiner triple system (STS) of a given order. An STS which attains this maximum for a given order is said to be maxi-Pasch. We show that loop factorization preserves the maxi-Pasch property and find that the Steiner loops of all currently known maxi-Pasch Steiner triple systems have centre of maximum possible order.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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