{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T05:51:23Z","timestamp":1774417883269,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:p>The question of describing the automorphisms of [Formula: see text] for a free algebra [Formula: see text] in a certain variety was considered by different authors since 2002. In this paper, we consider this question for the class of all relatively free groups having only cyclic centralizers of non-trivial elements. We prove that each automorphism of the endomorphism semigroup [Formula: see text] of groups [Formula: see text] from this class is uniquely determined by its action on the subgroup of inner automorphisms [Formula: see text]. The obtained general result includes the following cases: absolutely free groups, free Burnside groups of odd period [Formula: see text], free groups of infinitely based varieties of Adian (the cardinality of the set of such varieties is continuum), and so on.<\/jats:p>","DOI":"10.1142\/s0218196718500108","type":"journal-article","created":{"date-parts":[[2018,1,25]],"date-time":"2018-01-25T10:31:03Z","timestamp":1516876263000},"page":"207-215","source":"Crossref","is-referenced-by-count":2,"title":["The automorphisms of endomorphism semigroups of relatively free groups"],"prefix":"10.1142","volume":"28","author":[{"given":"V. S.","family":"Atabekyan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Mechanics, Yerevan State University, Alex Manoogian 1, Yerevan 0025, Armenia"}]},{"given":"H. T.","family":"Aslanyan","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and High Technology, RAU, 123 Hovsep Emin Str. Yerevan 0051, Armenia"}]}],"member":"219","published-online":{"date-parts":[[2018,3,27]]},"reference":[{"key":"S0218196718500108BIB001","doi-asserted-by":"publisher","DOI":"10.1070\/IM1970v004n04ABEH000928"},{"key":"S0218196718500108BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66932-3"},{"key":"S0218196718500108BIB003","doi-asserted-by":"publisher","DOI":"10.1134\/S0081543815040045"},{"issue":"3","key":"S0218196718500108BIB004","doi-asserted-by":"crossref","first-page":"111","DOI":"10.3103\/S1068362317030013","volume":"52","author":"Adian S. I.","year":"2017","journal-title":"J. Contemp. Math. Anal."},{"key":"S0218196718500108BIB005","doi-asserted-by":"publisher","DOI":"10.1070\/IM8631"},{"key":"S0218196718500108BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196713500318"},{"key":"S0218196718500108BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196715500149"},{"key":"S0218196718500108BIB008","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-11.2.181"},{"key":"S0218196718500108BIB009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-01-06155-X"},{"key":"S0218196718500108BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196707003974"},{"key":"S0218196718500108BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-06923-5"},{"key":"S0218196718500108BIB012","volume-title":"Varieties of Groups","author":"Neumann H.","year":"1968"},{"key":"S0218196718500108BIB014","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610799008273"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,13]],"date-time":"2022-08-13T05:09:15Z","timestamp":1660367355000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3]]},"references-count":13,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2018,3,27]]},"published-print":{"date-parts":[[2018,3]]}},"alternative-id":["10.1142\/S0218196718500108"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500108","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3]]}}}