{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T05:19:23Z","timestamp":1740028763661,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"abstract":"<jats:p>Let X and Y be compact Riemann surfaces and let &amp;phgr; : X &amp;rArr; Y be a ramified covering of a finite degree n. Let &amp;Pscr;Y&amp;sub; Y be a finite set of points that includes all branch points of &amp;phgr; and let &amp;Pscr;X= &amp;phgr;&amp;minus;1(&amp;Pscr;Y). Let X0= X \\ &amp;Pscr;Xand Y0= Y \\ &amp;Pscr;Y. Pick a base point y &amp;isin; Y0and let x &amp;isin; &amp;phgr;&amp;minus;1(y). Since the restriction of &amp;phgr; to X0is a covering, it induces an embedding &amp;phgr;&amp;ast;of &amp;pi;1(X0, x) into &amp;pi;1(Y0, y) as a subgroup of index n. We describe an algorithm that, given canonical generators of &amp;pi;1(Y0, y), computes canonical generators of &amp;pi;1(X0, x). The monodromy group G of the covering &amp;phgr; is naturally isomorphic to the factor group of &amp;pi;1(Y0, y) over its largest normal subgroup contained in &amp;phgr;&amp;ast;(&amp;pi;1(X0, x)). In light of this our algorithm can be used to compute standard generators for subgroups of G. The algorithm is implemented in GAP, and it was used to determine the containment among the Hurwitz loci of Riemann surfaces of low genus.<\/jats:p>","DOI":"10.3233\/978-1-60750-019-3-174","type":"book-chapter","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T19:11:46Z","timestamp":1739992306000},"source":"Crossref","is-referenced-by-count":0,"title":["A variant of the Reidemeister&amp;ndash;Schreier algorithm for the fundamental groups of Riemann surfaces"],"prefix":"10.3233","author":[{"family":"Magaard K.","sequence":"additional","affiliation":[]},{"family":"Shpectorov S.","sequence":"additional","affiliation":[]}],"member":"7437","container-title":["NATO Science for Peace and Security Series - D: Information and Communication Security","Algebraic Aspects of Digital Communications"],"original-title":[],"deposited":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T19:19:01Z","timestamp":1739992741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISSNISBN&issn=1874-6268&volume=24&spage=174"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-60750-019-3-174","relation":{},"ISSN":["1874-6268"],"issn-type":[{"value":"1874-6268","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}