{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T15:04:34Z","timestamp":1775747074133,"version":"3.50.1"},"reference-count":56,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"crossref","award":["EP\/R014604\/1"],"award-info":[{"award-number":["EP\/R014604\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p> We say that a finite group G satisfies the independence property if, for every pair of distinct elements x and y of G, either [Formula: see text] is contained in a minimal generating set for G or one of x and y is a power of the other. We give a complete classification of the finite groups with this property, and in particular prove that every such group is supersoluble. A key ingredient of our proof is a theorem showing that all but three finite almost simple groups H contain an element s such that the maximal subgroups of H containing s, but not containing the socle of H, are pairwise non-conjugate. <\/jats:p>","DOI":"10.1142\/s021819672350025x","type":"journal-article","created":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T06:33:45Z","timestamp":1678430025000},"page":"509-545","source":"Crossref","is-referenced-by-count":3,"title":["Finite groups satisfying the independence property"],"prefix":"10.1142","volume":"33","author":[{"given":"Saul D.","family":"Freedman","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK"}]},{"given":"Andrea","family":"Lucchini","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Padova, Dipartimento di Matematica, \u201cTullio Levi-Civita\u201d Via Trieste 63, 35121 Padova, Italy"}]},{"given":"Daniele","family":"Nemmi","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Padova, Dipartimento di Matematica, \u201cTullio Levi-Civita\u201d Via Trieste 63, 35121 Padova, Italy"}]},{"given":"Colva M.","family":"Roney-Dougal","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK"}]}],"member":"219","published-online":{"date-parts":[[2023,4,29]]},"reference":[{"issue":"9","key":"S021819672350025XBIB001","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1002\/mana.201900144","volume":"293","author":"Acciarri C.","year":"2020","journal-title":"Math. 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