Some Involutions which Generate the Finite Symmetric Group

Year 2020, Volume: 8 Issue: 1 , 25 - 28 , 20.03.2020

Leyla Bugay

https://doi.org/10.36753/mathenot.608443

Cited By: 4

https://izlik.org/JA28HD24KG

Abstract

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

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