Special subgroups of regular semigroups
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Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.
Blyth , T S & Almeida Santos , M H 2017 , ' Special subgroups of regular semigroups ' Communications in Algebra , vol 45 , no. 10 , pp. 4246-4256 . DOI: 10.1080/00927872.2016.1262385
Communications in Algebra
© 2017, Taylor & Francis. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.tandfonline.com / http://dx.doi.org/10.1080/00927872.2016.1262385
DescriptionThis work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA).
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