{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T19:59:26Z","timestamp":1648756766596},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> A group G is said to have finite section p-rankr<jats:sub>p<\/jats:sub>(G) = r (here p is a prime) if every elementary abelian p-section U\/V of G is finite of order at most p<jats:sup>r<\/jats:sup> and there is an elementary abelian p-section A\/B of G such that |A\/B| = p<jats:sup>r<\/jats:sup>. If \u2119 is the set of all primes and \u03bb : \u2119 \u2192 \u2115 \u222a {0} is a function, we say that a group G has \u03bb-bounded section rank if r<jats:sub>p<\/jats:sub>(G) \u2264 \u03bb(p) for each p \u2208 \u2119. In this paper we show that if G is a locally generalized radical group in which the normal closures of the cyclic subgroups of G have finite \u03bb-bounded section rank, then [G,G] has [Formula: see text]-bounded section rank for some function [Formula: see text]. This is a wide generalization of some results by Neumann, Smith and many others. Moreover we are able to give explicit formulas for the involved bounds. <\/jats:p>","DOI":"10.1142\/s0218196712500324","type":"journal-article","created":{"date-parts":[[2012,2,5]],"date-time":"2012-02-05T19:47:00Z","timestamp":1328471220000},"page":"1250032","source":"Crossref","is-referenced-by-count":0,"title":["GROUPS IN WHICH THE NORMAL CLOSURES OF CYCLIC SUBGROUPS HAVE FINITE SECTION RANK"],"prefix":"10.1142","volume":"22","author":[{"given":"LEONID A.","family":"KURDACHENKO","sequence":"first","affiliation":[{"name":"Department of Algebra, National University of Dnepropetrovsk, Vul. Naukova 13, Dnepropetrvsk 50, 49050, Ukraine"}]},{"given":"JOS\u00c9 M.","family":"MU\u00d1OZ-ESCOLANO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain"}]},{"given":"JAVIER","family":"OTAL","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","first-page":"297","volume":"41","author":"Charin V. S.","journal-title":"Mat. Sbornik"},{"key":"rf2","volume-title":"Representation Theory of Finite Groups and Associative algebras","author":"Curtis C. W.","year":"1962"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s11587-007-0004-7"},{"key":"rf4","first-page":"23","volume":"4","author":"Dixon M. 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