Skip to content

Research at St Andrews

On the number of subsemigroups of direct products involving the free monogenic semigroup

Research output: Contribution to journalArticle

Abstract

The direct product ℕ x ℕ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for ℕ x S, where S is a finite semigroup. It contains only countably manypairwise non-isomorphic subsemigroups if and only if S is a union of groups. And it contains only countably many pairwise nonisomorphic subdirect products if and only if every element of S has a relative left or right identity element.
Close

Details

Original languageEnglish
Number of pages12
JournalJournal of the Australian Mathematical Society
VolumeFirst View
Early online date1 Feb 2019
DOIs
Publication statusE-pub ahead of print - 1 Feb 2019

    Research areas

  • Subdirect product, Subsemigroup, Free mongenic semigroup

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Right noetherian semigroups

    Miller, C. & Ruskuc, N., 4 Aug 2019, (Accepted/In press) In : International Journal of Algebra and Computation. In press

    Research output: Contribution to journalArticle

  2. Presentations for subrings and subalgebras of finite co-rank

    Mayr, P. & Ruskuc, N., 20 Jul 2019, (Accepted/In press) In : Quarterly Journal of Mathematics.

    Research output: Contribution to journalArticle

  3. Rationality for subclasses of 321-avoiding permutations

    Albert, M. H., Brignall, R., Ruskuc, N. & Vatter, V., May 2019, In : European Journal of Combinatorics. 78, p. 44-72

    Research output: Contribution to journalArticle

  4. Generating subdirect products

    Mayr, P. & Ruskuc, N., 9 Apr 2019, In : Journal of the London Mathematical Society. Early View

    Research output: Contribution to journalArticle

  5. An introduction to presentations of monoid acts: quotients and subacts

    Miller, C. & Ruskuc, N., 27 Jan 2019, In : Communications in Algebra. Latest Articles

    Research output: Contribution to journalArticle

Related by journal

  1. L.G. Kovács and linear groups

    Detinko, A. S. & Flannery, D. L., Feb 2017, In : Journal of the Australian Mathematical Society. 102, 1, p. 55-62

    Research output: Contribution to journalArticle

  2. On the generating graph of a simple group

    Lucchini, A., Maroti, A. & Roney-Dougal, C. M., Aug 2017, In : Journal of the Australian Mathematical Society. 103, 1, p. 91-103

    Research output: Contribution to journalArticle

  3. Presentations of inverse semigroups, their kernels and extensions

    Carvalho, C. A., Gray, R. & Ruskuc, N., 1 Jun 2011, In : Journal of the Australian Mathematical Society. 90, 3, p. 289-316

    Research output: Contribution to journalArticle

  4. Growth of generating sets for direct powers of classical algebraic structures

    Quick, M. & Ruskuc, N., Aug 2010, In : Journal of the Australian Mathematical Society. 89, 1, p. 105-126 22 p.

    Research output: Contribution to journalArticle

ID: 256432336