{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T21:53:36Z","timestamp":1784584416385,"version":"3.55.0"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2004,2]]},"abstract":"<jats:p> A partial action of a group G on a set X is a weakening of the usual notion of a group action: the function G\u00d7X\u2192X that defines a group action is replaced by a partial function; in addition, the existence of g\u00b7(h\u00b7x) implies the existence of (gh)\u00b7x, but not necessarily conversely. Such partial actions are extremely widespread in mathematics, and the main aim of this paper is to prove two basic results concerning them. First, we obtain an explicit description of Exel's universal inverse semigroup [Formula: see text], which has the property that partial actions of the group G give rise to actions of the inverse semigroup [Formula: see text]. We apply this result to the theory of graph immersions. Second, we prove that each partial group action is the restriction of a universal global group action. We describe some applications of this result to group theory and the theory of E-unitary inverse semigroups. <\/jats:p>","DOI":"10.1142\/s0218196704001657","type":"journal-article","created":{"date-parts":[[2004,3,11]],"date-time":"2004-03-11T10:28:46Z","timestamp":1079000926000},"page":"87-114","source":"Crossref","is-referenced-by-count":104,"title":["PARTIAL ACTIONS OF GROUPS"],"prefix":"10.1142","volume":"14","author":[{"given":"J.","family":"KELLENDONK","sequence":"first","affiliation":[{"name":"Institut Girard Desargues, Universit\u00e9 Claude Bernard Lyon 1, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MARK V.","family":"LAWSON","sequence":"additional","affiliation":[{"name":"School of Informatics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd LL57 1UT, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1146-4"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90092-6"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90199-3"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196701000449"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-98-04575-4"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02773004"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01299742"},{"key":"rf8","volume-title":"An Introduction to Semigroup Theory","author":"Howie J. 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