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Largeness of the set of finite products in a semigroup

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Abstract

We investigate when the set of finite products of distinct terms of a sequence 〈x n 〉 ∞ n=1 in a semigroup (S,⋅) is large in any of several standard notions of largeness. These include piecewise syndetic, central, syndetic, central*, and IP*. In the case of a “nice” sequence in (S,⋅)=(ℕ,+) one has that FS(〈x n 〉 ∞ n=1 ) has any or all of the first three properties if and only if {x n+1−∑ n t=1 x t :n∈ℕ} is bounded from above.

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Authors and Affiliations

  1. Department of Mathematics, Howard University, Washington, DC, 20059, USA

    Chase Adams III & Neil Hindman

  2. Mathematics Centre, University of Hull, Hull, HU6, 7RX, UK

    Dona Strauss

Authors
  1. Chase Adams III
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  2. Neil Hindman
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  3. Dona Strauss
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Corresponding author

Correspondence to Chase Adams III.

Additional information

Communicated by Jimmie D. Lawson

N. Hindman acknowledges support received from the National Science Foundation via Grant DMS-0554803.

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Adams, C., Hindman, N. & Strauss, D. Largeness of the set of finite products in a semigroup. Semigroup Forum 76, 276–296 (2008). https://doi.org/10.1007/s00233-007-9006-8

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  • DOI: https://doi.org/10.1007/s00233-007-9006-8

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