Abstract
In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T <= S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappings. The subsemigroups T that we consider are of one of the following types: left zero, fight zero, completely simple. or inverse. Furthermore, we find the largest size of such subsemigroups U where the least rank of an element in U is specified. Numerous examples are given. (C) 2007 Elsevier B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 4801-4810 |
| Number of pages | 10 |
| Journal | Discrete Mathematics |
| Volume | 308 |
| Issue number | 20 |
| DOIs | |
| Publication status | Published - 28 Oct 2008 |
Keywords
- transformation semigroups
- completely simple semigroups
- inverse semigroups
- SEMIGROUPS
- SUBGROUPS
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