Some Involutions which Generate the Finite Symmetric Group

Let $S_{n}$ be the symmetric group on $X_{n}=\{1, \dots, n\}$, for $n\geq 2$. In this paper we state some properties of subsemigroups generated by two involutions (a permutation with degree $2$) $\alpha,\beta$ such that $\alpha\beta$ is an $n$-cycle, and then state some generating sets of $S_n$ consists of involutions.

Keywords:

Symmetric group, involution generating set,

PDF

___

Ay\i k, G., Ay\i k, H., Bugay, L. and Kelekci, O., Generating sets of finite singular transformation semigroups, Semigroup Forum, 86 (2013), 59--66.
Bugay, L., Quasi-idempotent ranks of some permutation groups and transformation semigroups, Turk. J. Math., Accepted.
Ganyushkin, O. and Mazorchuk, V., Classical Finite Transformation Semigroups, Springer-Verlag, London, 2009.
Garba, G. U., Idempotents in partial transformation semigroups, Proc. Royal Soc. Edinburgh, 116A (1990), 359--366.
Garba, G. U., On the idempotent ranks of certain semigroups of order-preserving transformations,. Portugal. Math., 51 (1994) 185--204.
Garba, G. U. and Imam, A. T., Products of quasi-idempotents in finite symmetric inverse semigroups, Semigroup Forum, 92 (2016), 645--658.
Howie, J. M., Idempotent generators in finite full transformation semigroups, Proc. Royal Soc. Edinburgh, 81A (1978), 317--323.
Howie, J. M., Fundamentals of Semigroup Theory, New York, Oxford University Press, 1995.
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: -

Arşiv