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SM ISO690:2012 KUZNETSOV, Eugene. Infinite sharply 2-transitive permutation groups. In: Conference of Mathematical Society of the Republic of Moldova, 28 iunie - 2 iulie 2017, Chişinău. Chişinău: Centrul Editorial-Poligrafic al USM, 2017, 4, pp. 105-108. ISBN 978-9975-71-915-5. |
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Conference of Mathematical Society of the Republic of Moldova 4, 2017 |
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Conferința "Conference of Mathematical Society of the Republic of Moldova" Chişinău, Moldova, 28 iunie - 2 iulie 2017 | ||||||
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Pag. 105-108 | ||||||
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Sharply 2-transitive permutation groups are studied in this work. The notions of transversal in a group [3] and Sabinin’s semidirect product [5] are used. All elements of order 2 from a sharply 2-transitive permutation group G form a loop transversal T in G to H0 = St0(G). For an arbitrary element ti ∈ T (ti 6= id) its centralizer Ci = CG(ti) is a group transversal in G to H0 = St0(G). The group G may be represented as a semidirect product: G = T ⋋ H0 = Ci ⋋ H0. A construction of the group G as an external semidirect product of two suitable groups is described. It gives us a potential example of an infinite sharply 2-transitive permutation group G with a non-abelian normal subgroup T , which consists of fixed-point-free permutations and the identity permutation. |
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Cuvinte-cheie permutation group, semidirect product, centralizer, loop, transversal |
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