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Chains of subsemigroups

Cameron, Peter J.; Gadouleau, Maximilien; Mitchell, James D.; Peresse, Yann

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Peter J. Cameron

James D. Mitchell

Yann Peresse


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.


Cameron, P. J., Gadouleau, M., Mitchell, J. D., & Peresse, Y. (2017). Chains of subsemigroups. Israel Journal of Mathematics, 220(1), 479-508.

Journal Article Type Article
Acceptance Date Aug 7, 2016
Online Publication Date May 8, 2017
Publication Date Jun 1, 2017
Deposit Date Aug 26, 2016
Publicly Available Date May 8, 2018
Journal Israel Journal of Mathematics
Print ISSN 0021-2172
Electronic ISSN 1565-8511
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 220
Issue 1
Pages 479-508


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