{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T08:28:43Z","timestamp":1777451323779,"version":"3.51.4"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p>For a compact surface \u03a3 (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix \u212c, of any family \u212c of endomorphisms of \u03c0<jats:sub>1<\/jats:sub>(\u03a3) is compressed in \u03c0<jats:sub>1<\/jats:sub>(\u03a3), i.e. rk ( Fix \u212c) \u2264 rk (H) for any subgroup Fix \u212c \u2264 H \u2264 \u03c0<jats:sub>1<\/jats:sub>(\u03a3). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that rk ( Fix \u03d5) \u2264 rk (G) for every \u03d5 \u2208 Aut (G).<\/jats:p>","DOI":"10.1142\/s0218196715500228","type":"journal-article","created":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T04:13:53Z","timestamp":1433391233000},"page":"865-887","source":"Crossref","is-referenced-by-count":8,"title":["Fixed subgroups are compressed in surface groups"],"prefix":"10.1142","volume":"25","author":[{"given":"Qiang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China"}]},{"given":"Enric","family":"Ventura","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics III, Universitat Polit\u00e8cnica de Catalunya, Manresa, Barcelona 08242, Catalonia, Spain"}]},{"given":"Jianchun","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Soochow University, Suzhou 215006, P. R. 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