Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/30507
DC Field | Value | Language |
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dc.contributor.author | Dolinka Igor | - |
dc.contributor.author | Gould Victoria | - |
dc.contributor.author | Yang Dandan | - |
dc.date.accessioned | 2020-12-14T18:30:35Z | - |
dc.date.available | 2020-12-14T18:30:35Z | - |
dc.date.issued | 2015 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | https://open.uns.ac.rs/handle/123456789/30507 | - |
dc.description.abstract | © 2015 Elsevier Inc. The study of the free idempotent generated semigroup IG(E) over a biordered set E began with the seminal work of Nambooripad in the 1970s and has seen a recent revival with a number of new approaches, both geometric and combinatorial. Here we study IG(E) in the case E is the biordered set of a wreath product G{wreath product}Tn, where G is a group and Tn is the full transformation monoid on n elements. This wreath product is isomorphic to the endomorphism monoid of the free G-act EndFn(G) on n generators, and this provides us with a convenient approach. We say that the rank of an element of EndFn(G) is the minimal number of (free) generators in its image. Let ε=ε2∈EndFn(G). For rather straightforward reasons it is known that if rankε=n-1 (respectively, n), then the maximal subgroup of IG(E) containing ε is free (respectively, trivial). We show that if rankε=r where 1≤r≤n-2, then the maximal subgroup of IG(E) containing ε is isomorphic to that in EndFn(G) and hence to G{wreath product}Sr, where Sr is the symmetric group on r elements. We have previously shown this result in the case r=1; however, for higher rank, a more sophisticated approach is needed. Our current proof subsumes the case r=1 and thus provides another approach to showing that any group occurs as the maximal subgroup of some IG(E). On the other hand, varying r again and taking G to be trivial, we obtain an alternative proof of the recent result of Gray and Ruškuc for the biordered set of idempotents of Tn. | - |
dc.language.iso | en | - |
dc.relation.ispartof | Journal of Algebra | - |
dc.source | CRIS UNS | - |
dc.source.uri | http://cris.uns.ac.rs | - |
dc.title | Free idempotent generated semigroups and endomorphism monoids of free G-acts | - |
dc.type | Journal/Magazine Article | - |
dc.identifier.doi | 10.1016/j.jalgebra.2014.12.041 | - |
dc.identifier.scopus | 2-s2.0-84923035759 | - |
dc.identifier.url | https://www.cris.uns.ac.rs/record.jsf?recordId=93147&source=BEOPEN&language=en | - |
dc.identifier.url | https://api.elsevier.com/content/abstract/scopus_id/84923035759 | - |
dc.relation.lastpage | 176 | - |
dc.relation.firstpage | 133 | - |
dc.relation.volume | 429 | - |
dc.identifier.externalcrisreference | (BISIS)93147 | - |
item.grantfulltext | none | - |
item.fulltext | No Fulltext | - |
crisitem.author.dept | Prirodno-matematički fakultet, Departman za matematiku i informatiku | - |
crisitem.author.orcid | 0000-0002-8644-0626 | - |
crisitem.author.parentorg | Prirodno-matematički fakultet | - |
Appears in Collections: | PMF Publikacije/Publications |
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