{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T21:57:36Z","timestamp":1777672656269,"version":"3.51.4"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p> For a finite group [Formula: see text], let [Formula: see text] denote the sum of element orders of [Formula: see text]. If [Formula: see text] is a positive integer let [Formula: see text] be the cyclic group of order [Formula: see text]. It is known that [Formula: see text] is the maximum value of [Formula: see text] on the set of groups of order [Formula: see text], and [Formula: see text] if and only if [Formula: see text] is cyclic of order [Formula: see text]. In this paper, we investigate the second largest value of [Formula: see text] on the set of groups of order [Formula: see text] and the structure of groups [Formula: see text] of order [Formula: see text] with this value of [Formula: see text] when [Formula: see text] is odd. <\/jats:p>","DOI":"10.1142\/s021819672140004x","type":"journal-article","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T14:38:35Z","timestamp":1623767915000},"page":"1049-1063","source":"Crossref","is-referenced-by-count":2,"title":["Sums of element orders in groups of odd order"],"prefix":"10.1142","volume":"31","author":[{"given":"Marcel","family":"Herzog","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel"}]},{"given":"Patrizia","family":"Longobardi","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Salerno, via Giovanni Paolo II, 132, Fisciano (Salerno) 84084, Italy"}]},{"given":"Mercede","family":"Maj","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Salerno, via Giovanni Paolo II, 132, Fisciano (Salerno) 84084, Italy"}]}],"member":"219","published-online":{"date-parts":[[2021,6,14]]},"reference":[{"key":"S021819672140004XBIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811004057"},{"key":"S021819672140004XBIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2010.537290"},{"key":"S021819672140004XBIB003","doi-asserted-by":"publisher","DOI":"10.1080\/00927870802502530"},{"key":"S021819672140004XBIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2018.09.009"},{"key":"S021819672140004XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2017.07.015"},{"key":"S021819672140004XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2018.06.015"},{"key":"S021819672140004XBIB008","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2018.1527924"},{"key":"S021819672140004XBIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2020.106531"},{"key":"S021819672140004XBIB010","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2011.653070"},{"issue":"3","key":"S021819672140004XBIB011","first-page":"501","volume":"39","author":"Amiri S. M. Jafarian","year":"2013","journal-title":"Bull. Iran. Math. Soc."},{"issue":"2","key":"S021819672140004XBIB012","first-page":"35","volume":"2","author":"Amiri S. M. Jafarian","year":"2013","journal-title":"Int. J. Group Theory"},{"key":"S021819672140004XBIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2013.07.003"},{"key":"S021819672140004XBIB014","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2013.839697"},{"key":"S021819672140004XBIB015","doi-asserted-by":"publisher","DOI":"10.5486\/PMD.2015.5961"},{"key":"S021819672140004XBIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s40840-016-0353-z"},{"key":"S021819672140004XBIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498813500266"},{"key":"S021819672140004XBIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8594-1"},{"key":"S021819672140004XBIB019","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2014.900686"},{"key":"S021819672140004XBIB020","first-page":"1","volume":"60","author":"T\u0103rn\u0103uceanu M.","year":"2014","journal-title":"Sci. Ann. Univ. \u201cA.I. Cuza\u201d Iasi Ser. Math."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819672140004X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T18:32:22Z","timestamp":1630953142000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819672140004X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,14]]},"references-count":19,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["10.1142\/S021819672140004X"],"URL":"https:\/\/doi.org\/10.1142\/s021819672140004x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,14]]}}}