Al-aadhami, Asawer (2017) Combinatorial Questions for $S\wr_{n} \mathcal{T}_n$ for a semigroup. PhD thesis, University of York.
Abstract
We study combinatorial questions for the wreath product $S\wr_{n}\mathcal{T}_{n}$ (properly, $S\wr_{\underline{n}}\mathcal{T}_{n}$) and related semigroups, where $S$ is a monoid and $\mathcal{T}_n$ is the full transformation monoid on $\underline{n}=\{ 1,2,\hdots, n\}$. It is well known that $S\wr_{n}\mathcal{T}_{n}$ is isomorphic to the endomorphism monoid of a free $S$-act $F_{n}(S)$ on $n$ generators and if $S$ is a group, $F_{n}(S)$ is an example of an independence algebra.
We determine the number of idempotents of $S\wr_{n}\mathcal{T}_{n}$, first in the more straightforward case where $S$ is a group.
We investigate the monoid of partial endomorphisms $\mathcal{PT}_{{\bf A}}$ of an independence algebra ${\bf A}$, focussing on the special case where $\bf A$ is
$\bf{F_{n}(G)}$. We determine Green's relations and Green's pre-orders on $\mathcal{PT}_{{\bf F_{n}(G)}}$. We also obtain formulae for the number of idempotents and the number of nilpotents in $\mathcal{PT}_{{\bf F_{n}(G)}}$.
We specialise Lavers' technique in order to construct a presentation for $M^{n}\rtimes \mathcal{T}_{n}$ from presentations of $M^{n}$ and $\mathcal{T}_{n}$.
Metadata
Supervisors: | Gould, Victoria |
---|---|
Awarding institution: | University of York |
Academic Units: | The University of York > Mathematics (York) |
Identification Number/EthosID: | uk.bl.ethos.736596 |
Depositing User: | MRS Asawer Al-aadhami |
Date Deposited: | 26 Feb 2018 16:00 |
Last Modified: | 25 Mar 2021 16:47 |
Open Archives Initiative ID (OAI ID): | oai:etheses.whiterose.ac.uk:19494 |
Download
Examined Thesis (PDF)
Filename: asawer-thesis-v2.pdf
Licence:
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License
Export
Statistics
You do not need to contact us to get a copy of this thesis. Please use the 'Download' link(s) above to get a copy.
You can contact us about this thesis. If you need to make a general enquiry, please see the Contact us page.