Generators and ranks in finite partial transformation semigroups

• Published in: Algebra and Discrete Mathematics
• Date: 2017
• ISSN: 1726-3255
• Main Authors: Garba, G.U., Imam, A.T.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156026
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Generators and ranks in finite partial transformation semigroups / G.U. Garba, A.T. Imam // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 237-248. — Бібліогр.: 16 назв. — англ.

We extend the concept of path-cycle, to the semigroup Pn, of all partial maps on Xn={1,2,…,n}, and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of Pn by means of path-cycles. The device is used to obtain information about generating sets for...