{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T10:57:26Z","timestamp":1758279446637},"reference-count":45,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2014,10,31]],"date-time":"2014-10-31T00:00:00Z","timestamp":1414713600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2014,10,31]],"date-time":"2014-10-31T00:00:00Z","timestamp":1414713600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of the London Mathematical Society"],"published-print":{"date-parts":[[2014,12]]},"DOI":"10.1112\/jlms\/jdu056","type":"journal-article","created":{"date-parts":[[2014,11,2]],"date-time":"2014-11-02T00:18:04Z","timestamp":1414887484000},"page":"879-902","source":"Crossref","is-referenced-by-count":5,"title":["Pseudo-reflection groups and essential dimension"],"prefix":"10.1112","volume":"90","author":[{"given":"Alexander","family":"Duncan","sequence":"first","affiliation":[]},{"given":"Zinovy","family":"Reichstein","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2014,10,31]]},"reference":[{"key":"10.1112\/jlms\/jdu056-BIB1|citC1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/978-3-319-05254-0_16","article-title":"Finite simple groups of small essential dimension","volume-title":"Trends in contemporary mathematics","author":"Beauville","year":"2014"},{"key":"10.1112\/jlms\/jdu056-BIB2|citC2","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/0021-8693(71)90044-5","article-title":"Finite groups whose Sylow subgroups are abelian","volume":"17","author":"Broshi","year":"1971","journal-title":"J. Algebra"},{"key":"10.1112\/jlms\/jdu056-BIB3|citC3","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1023\/A:1000144403695","article-title":"On the essential dimension of a finite group","volume":"106","author":"Buhler","year":"1997","journal-title":"Compos. Math."},{"key":"10.1112\/jlms\/jdu056-BIB4|citC4","first-page":"127","article-title":"On Tschirnhaus transformations","volume-title":"Topics in number theory (University Park, PA, 1997)","author":"Buhler","year":"1999"},{"key":"10.1112\/jlms\/jdu056-BIB5|citC5","unstructured":"F. Charles B. Poonen Bertini irreducibility theorems over finite fields"},{"key":"10.1112\/jlms\/jdu056-BIB6|citC6","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1017\/S0305004100060746","article-title":"The Coxeter-Todd lattice, the Mitchell group, and related sphere packings","volume":"93","author":"Conway","year":"1983","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"10.1112\/jlms\/jdu056-BIB7|citC7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-04958-7","volume-title":"Computational invariant theory","author":"Derksen","year":"2002"},{"key":"10.1112\/jlms\/jdu056-BIB8|citC8","first-page":"283","article-title":"Weyl groups and Cremona transformations","volume-title":"Singularities, Part 1 (Arcata, CA, 1981)","author":"Dolgachev","year":"1983"},{"key":"10.1112\/jlms\/jdu056-BIB9|citC9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-07-01190-1","article-title":"Reflection groups in algebraic geometry","volume":"45","author":"Dolgachev","year":"2008","journal-title":"Bull. Amer. Math. Soc. (N.S.)"},{"key":"10.1112\/jlms\/jdu056-BIB10|citC10","volume-title":"Point sets in projective spaces and theta functions","author":"Dolgachev","year":"1988"},{"key":"10.1112\/jlms\/jdu056-BIB11|citC11","doi-asserted-by":"crossref","first-page":"263","DOI":"10.4310\/MRL.2010.v17.n2.a5","article-title":"Essential dimensions of A7 and S7","volume":"17","author":"Duncan","year":"2010","journal-title":"Math. Res. Lett."},{"key":"10.1112\/jlms\/jdu056-BIB12|citC12","article-title":"Versality of algebraic group actions and rational points on twisted varieties","author":"Duncan","journal-title":"J. Algebraic Geom."},{"key":"10.1112\/jlms\/jdu056-BIB13|citC13","doi-asserted-by":"crossref","first-page":"399","DOI":"10.4064\/aa-21-1-399-408","article-title":"On a linear diophantine problem of Frobenius","volume":"21","author":"Erd\u00f6s","year":"1972","journal-title":"Acta Arith."},{"key":"10.1112\/jlms\/jdu056-BIB14|citC14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02421-8","volume-title":"Intersection theory","author":"Fulton","year":"1984"},{"key":"10.1112\/jlms\/jdu056-BIB15|citC15","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1017\/S0027763000023023","article-title":"Note on A-groups","volume":"4","author":"It\u00f4","year":"1952","journal-title":"Nagoya Math. J."},{"key":"10.1112\/jlms\/jdu056-BIB16|citC16","volume-title":"Generic polynomials","author":"Jensen","year":"2002"},{"key":"10.1112\/jlms\/jdu056-BIB17|citC17","volume-title":"Th\u00e9or\u00e8mes de Bertini et applications","author":"Jouanolou","year":"1983"},{"key":"10.1112\/jlms\/jdu056-BIB18|citC18","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3542-0","volume-title":"Reflection groups and invariant theory","author":"Kane","year":"2001"},{"key":"10.1112\/jlms\/jdu056-BIB19|citC19","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s00222-007-0106-6","article-title":"Essential dimension of finite p-groups","volume":"172","author":"Karpenko","year":"2008","journal-title":"Invent. Math."},{"key":"10.1112\/jlms\/jdu056-BIB20|citC20","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1080\/00927877908822375","article-title":"Bertini theorems for hypersurface sections containing a subscheme","volume":"7","author":"Kleiman","year":"1979","journal-title":"Comm. Algebra"},{"key":"10.1112\/jlms\/jdu056-BIB21|citC21","volume-title":"Vorlesungen \u00fcber das Ikosaeder und die Aufl\u00f6sung der Gleichungen vom f\u00fcnften Grade (Teubner, Leipzig, 1884)","author":"Klein","year":"1956"},{"key":"10.1112\/jlms\/jdu056-BIB22|citC22","doi-asserted-by":"crossref","first-page":"422","DOI":"10.4153\/CMB-2002-044-5","article-title":"On the essential dimension of some semi-direct products","volume":"45","author":"Ledet","year":"2002","journal-title":"Canad. Math. Bull."},{"key":"10.1112\/jlms\/jdu056-BIB23|citC23","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/S1631-073X(03)00192-4","article-title":"Invariant theory and eigenspaces for unitary reflection groups","volume":"336","author":"Lehrer","year":"2003","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"10.1112\/jlms\/jdu056-BIB24|citC24","volume-title":"Unitary reflection groups","author":"Lehrer","year":"2009"},{"key":"10.1112\/jlms\/jdu056-BIB25|citC25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/crelle.2012.010","article-title":"Essential dimension of algebraic tori","volume":"677","author":"L\u00f6tscher","year":"2013","journal-title":"J. reine angew. Math."},{"key":"10.1112\/jlms\/jdu056-BIB26|citC26","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1007\/s00031-011-9157-2","article-title":"Essential p-dimension of the normalizer of a maximal torus","volume":"16","author":"MacDonald","year":"2011","journal-title":"Transform. Groups"},{"key":"10.1112\/jlms\/jdu056-BIB27|citC27","volume-title":"Cubic forms. Algebra, geometry, arithmetic","author":"Manin","year":"1986"},{"key":"10.1112\/jlms\/jdu056-BIB28|citC28","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s00031-013-9216-y","article-title":"Essential dimension: a survey","volume":"18","author":"Merkurjev","year":"2013","journal-title":"Transform. Groups"},{"key":"10.1112\/jlms\/jdu056-BIB29|citC29","doi-asserted-by":"crossref","first-page":"467","DOI":"10.2140\/ant.2009.3.467","article-title":"The essential dimension of the normalizer of a maximal torus in the projective linear group","volume":"3","author":"Meyer","year":"2009","journal-title":"Algebra Number Theory"},{"key":"10.1112\/jlms\/jdu056-BIB30|citC30","first-page":"445","article-title":"Some consequences of the Karpenko-Merkurjev theorem","author":"Meyer","year":"2010","journal-title":"Doc. Math."},{"key":"10.1112\/jlms\/jdu056-BIB31|citC31","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/BFb0085883","article-title":"R\u00e9solution simultan\u00e9e de points doubles rationnels","volume-title":"S\u00e9minaire sur les Singularit\u00e9s des Surfaces","author":"Pinkham","year":"1980"},{"issue":"(2)","key":"10.1112\/jlms\/jdu056-BIB32|citC32","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.4007\/annals.2004.160.1099","article-title":"Bertini theorems over finite fields","volume":"160","author":"Poonen","year":"2004","journal-title":"Ann. of Math."},{"key":"10.1112\/jlms\/jdu056-BIB33|citC33","doi-asserted-by":"crossref","first-page":"265","DOI":"10.4310\/MRL.2008.v15.n2.a5","article-title":"Smooth hypersurface sections containing a given subscheme over a finite field","volume":"15","author":"Poonen","year":"2008","journal-title":"Math. Res. Lett."},{"key":"10.1112\/jlms\/jdu056-BIB34|citC34","first-page":"162","article-title":"Essential dimension","volume-title":"Proceedings of the International Congress of Mathematicians. Vol. II","author":"Reichstein","year":"2010"},{"key":"10.1112\/jlms\/jdu056-BIB35|citC35","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1090\/noti909","article-title":"What is \u2026ssential dimension?","volume":"59","author":"Reichstein","year":"2012","journal-title":"Notices Amer. Math. Soc."},{"key":"10.1112\/jlms\/jdu056-BIB36|citC36","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.4153\/CJM-2000-043-5","article-title":"Essential dimensions of algebraic groups and a resolution theorem for G-varieties, with an appendix by J. Kollar and E. Szabo","volume":"52","author":"Reichstein","year":"2000","journal-title":"Canad. J. Math."},{"key":"10.1112\/jlms\/jdu056-BIB37|citC37","doi-asserted-by":"crossref","first-page":"207","DOI":"10.2140\/pjm.2001.200.207","article-title":"Splitting fields of G-varieties","volume":"200","author":"Reichstein","year":"2001","journal-title":"Pacific J. Math."},{"key":"10.1112\/jlms\/jdu056-BIB38|citC38","article-title":"Groupes finis d\u2019automorphismes d\u2019anneaux locaux r\u00e9guliers","volume-title":"Colloque d\u2019Alg\u00e8bre (Paris, 1967)","author":"Serre","year":"1968"},{"key":"10.1112\/jlms\/jdu056-BIB39|citC39","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9458-7","volume-title":"Linear representations of finite groups","author":"Serre","year":"1977"},{"key":"10.1112\/jlms\/jdu056-BIB40|citC40","first-page":"1","article-title":"Cohomological invariants, Witt invariants, and trace forms","volume-title":"Cohomological invariants in Galois cohomology","author":"Serre","year":"2003"},{"key":"10.1112\/jlms\/jdu056-BIB41|citC41","doi-asserted-by":"crossref","first-page":"274","DOI":"10.4153\/CJM-1954-028-3","article-title":"Finite unitary reflection groups","volume":"6","author":"Shephard","year":"1954","journal-title":"Canad. J. Math."},{"key":"10.1112\/jlms\/jdu056-BIB42|citC42","first-page":"109","article-title":"Weierstrass transformations and cubic surfaces","volume":"44","author":"Shioda","year":"1995","journal-title":"Comment. Math. Univ. Sancti Pauli"},{"key":"10.1112\/jlms\/jdu056-BIB43|citC43","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF01390173","article-title":"Regular elements of finite reflection groups","volume":"25","author":"Springer","year":"1974","journal-title":"Invent. Math."},{"key":"10.1112\/jlms\/jdu056-BIB44|citC44","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1090\/S0002-9947-1964-0167535-3","article-title":"Differential equations invariant under finite reflection groups","volume":"112","author":"Steinberg","year":"1964","journal-title":"Trans. Amer. Math. Soc."},{"issue":"(2)","key":"10.1112\/jlms\/jdu056-BIB45|citC45","doi-asserted-by":"crossref","first-page":"405","DOI":"10.2307\/1970648","article-title":"The characterization of finite groups with abelian Sylow 2-subgroups","volume":"89","author":"Walter","year":"1969","journal-title":"Ann. of Math."}],"container-title":["Journal of the London Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1112%2Fjlms%2Fjdu056","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/onlinelibrary.wiley.com\/wol1\/doi\/10.1112\/jlms\/jdu056\/fullpdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T11:09:57Z","timestamp":1626779397000},"score":1,"resource":{"primary":{"URL":"http:\/\/doi.wiley.com\/10.1112\/jlms\/jdu056"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,31]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,12]]}},"URL":"https:\/\/doi.org\/10.1112\/jlms\/jdu056","archive":["Portico"],"relation":{},"ISSN":["0024-6107"],"issn-type":[{"value":"0024-6107","type":"print"}],"subject":[],"published":{"date-parts":[[2014,10,31]]}}}