Degtyarev, A.Salepci, N.2016-02-082016-02-0820130027-7630http://hdl.handle.net/11693/20919We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz fibration is algebraic. © 2013 by The Editorial Board of the Nagoya Mathematical Journal.EnglishArticle10.1215/00277630-2077026