{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:37Z","timestamp":1740120277303,"version":"3.37.3"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100006753","name":"CMUP","doi-asserted-by":"crossref","award":["UIBD\/MAT\/00144\/2020"],"award-info":[{"award-number":["UIBD\/MAT\/00144\/2020"]}],"id":[{"id":"10.13039\/501100006753","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p> Birget, Margolis, Meakin and Weil proved that a finitely generated subgroup K of a free group is pure if and only if the transition monoid M (K) of its Stallings automaton is aperiodic. In this paper, we establish further connections between algebraic properties of K and algebraic properties of M (K). We mainly focus on the cases where M (K) belongs to the pseudovariety of finite monoids all of whose subgroups lie in a given pseudovariety of finite groups. We also discuss normal, malnormal and cyclonormal subgroups of [Formula: see text] using the transition monoid of the corresponding Stallings automaton. <\/jats:p>","DOI":"10.1142\/s0218196723500224","type":"journal-article","created":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T13:06:41Z","timestamp":1677244001000},"page":"445-479","source":"Crossref","is-referenced-by-count":0,"title":["On the transition monoid of the Stallings automaton of a subgroup of a free group"],"prefix":"10.1142","volume":"33","author":[{"given":"In\u00eas F.","family":"Guimar\u00e3es","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, R. 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