Cancellative semigroups admitting conjugates
Abstract
We prove conjugate analogs of Mal’cev-Neumann-Taylor-Levi’s theorems. In other words, we characterize semigroups em- beddable in nilpotent groups of class n by means of conjugacy laws involving semigroup laws described by Mal’cev, Neumann and Taylor. Moreover we prove that a cancellative semigroup admitting conjugates is embeddable in a nilpotent group of class 2 if and only if it satisfies the conjugacy law x^y^z = x^y. Also adapting Ore’s techniques we describe an exact procedure for embedding a cancellative semigroup admitting conjugates into a group.
- Published
- 28 October 2015
- Volume
- 2015 (2015)
- License
- CC BY 3.0
Copyright © 2015 G.I. Moghaddam, R. Padmanabhan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
G. I. Moghaddam, R. Padmanabhan, Cancellative semigroups admitting conjugates, J. Semigroup Theory Appl. 2015 (2015), 9.
BibTeX
@article{Moghaddam2015,
author = {Moghaddam, G.I. and Padmanabhan, R.},
title = {Cancellative semigroups admitting conjugates},
journal = {J. Semigroup Theory Appl.},
volume = {2015},
year = {2015},
pages = {9},
doi = {}
}