{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T00:02:10Z","timestamp":1705017730072},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,8]]},"abstract":"<jats:p>The paper discusses the Andrews\u2013Curtis graph \u0394<jats:sub>k<\/jats:sub>(G,N) of a normal subgroup N in a group G. The vertices of the graph are k-tuples of elements in N which generate N as a normal subgroup; two vertices are connected if one of them can be obtained from another by certain elementary transformations. This object appears naturally in the theory of black box finite groups and in the Andrews\u2013Curtis conjecture in algebraic topology [3].<\/jats:p><jats:p>We suggest an approach to the Andrews\u2013Curtis conjecture based on the study of Andrews\u2013Curtis graphs of finite groups, discuss properties of Andrews\u2013Curtis graphs of some classes of finite groups and results of computer experiments with generation of random elements of finite groups by random walks on their Andrews\u2013Curtis graphs.<\/jats:p>","DOI":"10.1142\/s0218196703001468","type":"journal-article","created":{"date-parts":[[2003,11,21]],"date-time":"2003-11-21T08:49:01Z","timestamp":1069404541000},"page":"415-436","source":"Crossref","is-referenced-by-count":2,"title":["THE ANDREWS\u2013CURTIS CONJECTURE AND BLACK BOX GROUPS"],"prefix":"10.1142","volume":"13","author":[{"given":"ALEXANDRE V.","family":"BOROVIK","sequence":"first","affiliation":[{"name":"Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, United Kingdom"}]},{"given":"EVGENII I.","family":"KHUKHRO","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Novosibirsk-90, 630090, Russia"}]},{"given":"ALEXEI G.","family":"MYASNIKOV","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The City College of New York, New York, NY 10031, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1515\/9783110872743.1"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(85)90010-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1965-0173241-8"},{"key":"rf6","doi-asserted-by":"crossref","unstructured":"L.\u00a0Babai, Groups and Computations II, Randomization in group algorithms: conceptual questions\u00a028, eds. 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