Chains of subsemigroups
Date
06/2017Metadata
Show full item recordAbstract
We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite chains. In some cases, we give lower bounds for the total number of subsemigroups of these semigroups. We give general results for finite completely regular and finite inverse semigroups. Wherever possible, we state our results in the greatest generality; in particular, we include infinite semigroups where the result is true for these. The length of a subgroup chain in a group is bounded by the logarithm of the group order. This fails for semigroups, but it is perhaps surprising that there is a lower bound for the length of a subsemigroup chain in the full transformation semigroup which is a constant multiple of the semigroup order.
Citation
Cameron , P J , Gadouleau , M , Mitchell , J D & Peresse , Y 2017 , ' Chains of subsemigroups ' , Israel Journal of Mathematics , vol. 220 , no. 1 , pp. 479-508 . https://doi.org/10.1007/s11856-017-1523-x
Publication
Israel Journal of Mathematics
Status
Peer reviewed
ISSN
0021-2172Type
Journal article
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