Some Involutions which Generate the Finite Symmetric Group

Let Sn be the symmetric group on Xn = {1, . . . , n} for n ≥ 2. In this paper we state some propertiesof subsemigroups generated by two involutions (a permutation with degree 2) α, β such that αβ is ann-cycle, and then we state some generating sets of Sn which consists of involutions.

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[1] Ayık, G., Ayık, H., Bugay, L., Kelekci, O.: Generating sets of finite singular transformation semigroups. Semigroup Forum. 86, 59–66 (2013).
[2] Bugay, L.: Quasi-idempotent ranks of some permutation groups and transformation semigroups. Turk. J. Math. 43, 2390-2395 (2019).
[3] Ganyushkin, O., Mazorchuk, V.: Classical finite transformation semigroups. Springer-Verlag. London (2009).
[4] Garba, G. U.: Idempotents in partial transformation semigroups. Proc. Royal Soc. Edinburgh. 116A, 359–366 (1990).
[5] Garba, G. U.: On the idempotent ranks of certain semigroups of order-preserving transformations. Portugal. Math. 51, 185–204 (1994).
[6] Garba, G. U., Imam, A. T.: Products of quasi-idempotents in finite symmetric inverse semigroups. Semigroup Forum. 92, 645–658 (2016).
[7] Howie, J. M.: Idempotent generators in finite full transformation semigroups. Proc. Royal Soc. Edinburgh. 81A, 317–323 (1978).
[8] Howie, J. M.: Fundamentals of semigroup theory. Oxford University Press. New York (1995).
[9] Isaacs, I. M.: Finite group theory. American Mathematical Society, Graduate Studies in Mathematics, Volume 92. United States of America (2008).

Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

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