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Mat. Sb., 1995, Volume 186, Number 10, Pages 41–56 (Mi msb77)  

Classification of finite 3-nets of types I.3, I.4, I.5

A. P. Il'inykh

Urals State Pedagogical University

Abstract: Using the description of 2-transitive groups, in this paper finite 3-nets of types I.3, I.4, and I.5 are studied. According to the Barlotti-Strambach classification (see [4]) an arbitrary 3-net belongs to one of the seven Lenz classes I.1-I.5, II.1-II.2. In this work the question of the existence of nets of types I.3, I.4, I.5 remained open. The non-existence of a finite net of type I.5 is proved and the finite nets of type I.3 and I.4 are described up to isomorphism.

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English version:
Sbornik: Mathematics, 1995, 186:10, 1429–1443

Bibliographic databases:

UDC: 512.548.7
MSC: Primary 51E14, 51E26, 51A25; Secondary 20B25, 05B25, 20N05
Received: 12.10.1994

Citation: A. P. Il'inykh, “Classification of finite 3-nets of types I.3, I.4, I.5”, Mat. Sb., 186:10 (1995), 41–56; Sb. Math., 186:10 (1995), 1429–1443

Citation in format AMSBIB
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\by A.~P.~Il'inykh
\paper Classification of finite 3-nets of types I.3, I.4, I.5
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 10
\pages 41--56
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1361593}
\zmath{https://zbmath.org/?q=an:0865.51007}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 10
\pages 1429--1443
\crossref{https://doi.org/10.1070/SM1995v186n10ABEH000077}
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