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Mat. Zametki, 1972, Volume 12, Issue 5, Pages 605–616 (Mi mz9923)  

This article is cited in 2 scientific papers (total in 3 papers)

Loop geometries

L. V. Sabinin

Patrice Lumumba University

Abstract: We introduce the construction of the semidirect product of a loop and its associate (or quasigroup) — the group uniquely generated by the loop. For a (left or right) loop the semidirect product is a group acting transitively on the loop so that the loop is provided with the structure of a homogeneous space, the stationary subgroup being its associate. The construction is reversible, viz.: any homogeneous space can be provided with the structure of a loop so that the semidirect product of it with the transassociate is isomorphic with the fundamental group of the homogeneous space and the transassociate is isomorphic with the stationarity group.

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English version:
Mathematical Notes, 1972, 12:5, 799–805

Bibliographic databases:

UDC: 519.4
Received: 03.12.1971

Citation: L. V. Sabinin, “Loop geometries”, Mat. Zametki, 12:5 (1972), 605–616; Math. Notes, 12:5 (1972), 799–805

Citation in format AMSBIB
\Bibitem{Sab72}
\by L.~V.~Sabinin
\paper Loop geometries
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 5
\pages 605--616
\mathnet{http://mi.mathnet.ru/mz9923}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=340461}
\zmath{https://zbmath.org/?q=an:0258.20066}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 5
\pages 799--805
\crossref{https://doi.org/10.1007/BF01099069}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. V. Sabinin, “On the gyrogroups of Hungar”, Russian Math. Surveys, 50:5 (1995), 1095–1096  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Yu. E. Borovskii, V. A. Kudryavtsev, Yu. G. Reshetnyak, “Lev Vasil'evich Sabinin (obituary)”, Russian Math. Surveys, 61:5 (2006), 975–980  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Siberian Adv. Math., 23:3 (2013), 210–218  mathnet  crossref  mathscinet  elib
  • Математические заметки Mathematical Notes
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