{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T19:10:09Z","timestamp":1714417809926},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p>We define several \"standard\" subgroups of the automorphism group Aut (G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut (G). If C is the commutation graph of G, we show how Aut (G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decomposition of Aut (G) into a subgroup of locally conjugating automorphisms by the subgroup stabilizing a certain lattice of \"admissible subsets\" of the vertices of C. We then characterize those graphs for which Aut (G) is a product (not necessarily semi-direct) of two such subgroups.<\/jats:p>","DOI":"10.1142\/s0218196712500749","type":"journal-article","created":{"date-parts":[[2012,9,24]],"date-time":"2012-09-24T09:20:34Z","timestamp":1348478434000},"page":"1250074","source":"Crossref","is-referenced-by-count":3,"title":["AUTOMORPHISMS OF PARTIALLY COMMUTATIVE GROUPS II: COMBINATORIAL SUBGROUPS"],"prefix":"10.1142","volume":"22","author":[{"given":"ANDREW J.","family":"DUNCAN","sequence":"first","affiliation":[{"name":"School of Mathematics &amp; Statistics, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VLADIMIR N.","family":"REMESLENNIKOV","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Omsk State University, 55-A Prospect Mira, Omsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,12,3]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025913505208"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01895842"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.2307\/1970833"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-010-0062-3"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"541","DOI":"10.4171\/ggd\/69","volume":"3","author":"Bux K.-U.","journal-title":"Groups Geom. Dyn."},{"key":"rf6","series-title":"Memoirs of the American Mathematical Society","volume-title":"\"Abstract\" Homomorphisms of Split Kac\u2013Moody Groups","volume":"294","author":"Caprace P.-E.","year":"2009"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-007-9148-6"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2007.11.2227"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2012.12.979"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdn108"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/41.2.155"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2009.13.817"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671100608X"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196793000032"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-006-9046-3"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.08.032"},{"key":"rf19","first-page":"151","volume":"5","author":"Duncan A. J.","journal-title":"Sib. \u00c8lektron. Mat. Izv."},{"key":"rf20","doi-asserted-by":"crossref","first-page":"739","DOI":"10.4171\/ggd\/103","volume":"4","author":"Duncan A. J.","journal-title":"Groups Geom. Dyn."},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/378\/07014"},{"key":"rf22","first-page":"265","volume":"8","author":"Fouxe-Rabinovitch D. I.","journal-title":"Rec. Math. [Mat. Sbornik] N.S."},{"key":"rf23","first-page":"183","volume":"9","author":"Fouxe-Rabinovitch D. I.","journal-title":"Rec. Math. [Mat. Sbornik] N.S."},{"key":"rf24","first-page":"115","volume":"54","author":"Gilbert N. D.","journal-title":"Proc. London Math. Soc. 3"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000314"},{"key":"rf27","doi-asserted-by":"crossref","first-page":"125","DOI":"10.4171\/ggd\/153","volume":"6","author":"Gutierrez M.","journal-title":"Groups Geom. Dyn."},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1969-099-7"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/52.2.318"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74510-5_26"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1986-073-3"},{"key":"rf32","doi-asserted-by":"crossref","first-page":"335","DOI":"10.4171\/ggd\/160","volume":"6","author":"Minasyan A.","journal-title":"Groups Geom. Dyn."},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-00-05678-1"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1007\/s10469-010-9078-5"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90319-0"},{"key":"rf37","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1960-054-6"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500749","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T18:45:59Z","timestamp":1714416359000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11]]},"references-count":33,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2012,12,3]]},"published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.1142\/S0218196712500749"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500749","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11]]}}}