@article{DELUCA199491,
    Abstract = {Let S be a semigroup. For s, t ∈ S we set s ≤Bt if s ∈ {t} ∪ tS1t; we say that S satisfies the condition minB, if and only if any strictly descending chain w.r.t. ≤B of elements of S has a finite length. The main result of the paper is the following theorem: Let T be a semigroup satisfying minB. Let T′ be a subsemigroup of T such that all subgroups of T are locally finite in T′. Then T′ is locally finite. This result is a noteworthy generalization of a theorem of Coudrain and Sch{\"u}tzenberger. Moreover, as a corollary we obtain the theorem of McNaughton and Zalcstein which gives a positive answer to the Burnside problem for semigroups of matrices on a field.},
    Author = {Deluca, A. and Varricchio, S.},
    File = {A Finiteness Condition for Semigroups Generalizing a Theorem of Coudrain and Schützenberger - 1-s2.0-S000187088471067X-main.pdf},
    ISSN = {0001-8708},
    Journal = {Advances in Mathematics},
    Number = {1},
    Pages = {91-103},
    Title = {A Finiteness Condition for Semigroups Generalizing a Theorem of Coudrain and Sch{\"u}tzenberger},
    URL = {https://www.sciencedirect.com/science/article/pii/S000187088471067X},
    Volume = {108},
    Year = {1994},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S000187088471067X},
    bdsk-url-2 = {https://doi.org/10.1006/aima.1994.1067},
    date-added = {2023-08-31 10:26:39 +0200},
    date-modified = {2023-08-31 10:26:39 +0200},
    doi = {10.1006/aima.1994.1067}
}

@article{DELUCA199491, Abstract = {Let S be a semigroup. For s, t ∈ S we set s ≤Bt if s ∈ {t} ∪ tS1t; we say that S satisfies the condition minB, if and only if any strictly descending chain w.r.t. ≤B of elements of S has a finite length. The main result of the paper is the following theorem: Let T be a semigroup satisfying minB. Let T′ be a subsemigroup of T such that all subgroups of T are locally finite in T′. Then T′ is locally finite. This result is a noteworthy generalization of a theorem of Coudrain and Sch{\"u}tzenberger. Moreover, as a corollary we obtain the theorem of McNaughton and Zalcstein which gives a positive answer to the Burnside problem for semigroups of matrices on a field.}, Author = {Deluca, A. and Varricchio, S.}, File = {A Finiteness Condition for Semigroups Generalizing a Theorem of Coudrain and Schützenberger - 1-s2.0-S000187088471067X-main.pdf}, ISSN = {0001-8708}, Journal = {Advances in Mathematics}, Number = {1}, Pages = {91-103}, Title = {A Finiteness Condition for Semigroups Generalizing a Theorem of Coudrain and Sch{\"u}tzenberger}, URL = {https://www.sciencedirect.com/science/article/pii/S000187088471067X}, Volume = {108}, Year = {1994}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S000187088471067X}, bdsk-url-2 = {https://doi.org/10.1006/aima.1994.1067}, date-added = {2023-08-31 10:26:39 +0200}, date-modified = {2023-08-31 10:26:39 +0200}, doi = {10.1006/aima.1994.1067} }