{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T23:16:55Z","timestamp":1649027815490},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2014,3]]},"abstract":" We analyze the complexity of ascendant sequences in locally nilpotent groups, showing that if G is a computable locally nilpotent group and x0<\/jats:sub>, x1<\/jats:sub>, \u2026, xN<\/jats:sub> \u2208 G, N \u2208 \u2115, then one can always find a uniformly computably enumerable (i.e. uniformly [Formula: see text]) ascendant sequence of order type \u03c9 + 1 of subgroups in G beginning with \u3008x0<\/jats:sub>, x1<\/jats:sub>, \u2026, xN<\/jats:sub>\u3009G<\/jats:sub>, the subgroup generated by x0<\/jats:sub>, x1<\/jats:sub>, \u2026, xN<\/jats:sub> in G. This complexity is surprisingly low in light of the fact that the usual definition of ascendant sequence involves arbitrarily large ordinals that index sequences of subgroups defined via a transfinite recursion in which each step is incomputable. We produce this surprisingly low complexity sequence via the effective algebraic commutator collection process of P. Hall, and a related purely algebraic Normal Form Theorem of M. Hall for nilpotent groups. <\/jats:p>","DOI":"10.1142\/s0218196714500118","type":"journal-article","created":{"date-parts":[[2014,3,11]],"date-time":"2014-03-11T12:23:47Z","timestamp":1394540627000},"page":"189-205","source":"Crossref","is-referenced-by-count":1,"title":["The complexity of ascendant sequences in locally nilpotent groups"],"prefix":"10.1142","volume":"24","author":[{"given":"Chris J.","family":"Conidis","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA"}]},{"given":"Richard A.","family":"Shore","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA"}]}],"member":"219","published-online":{"date-parts":[[2014,4,10]]},"reference":[{"key":"rf1","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","author":"Ash C. 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