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In addition, we define standard generators for the groups under consideration, and exhibit black box algorithms for finding standard generators and checking whether given elements of the group are standard generators.","abstract_html":"Motivated by the World Wide Web Atlas of Finite Group Representations and the recent classification of low-dimensional representations of quasisimple groups in cross-characteristic fields by Hiss and Malle, we construct with a computer over 650 representations of finite simple groups. Explicit matrices for these representations are available on the Internet and are included on an attached CD-ROM. Our main tool is a GAP program for decomposing permutation modules. It uses reduction modulo various primes and rational reconstruction to give an acceptable performance. In addition, we define standard generators for the groups under consideration, and exhibit black box algorithms for finding standard generators and checking whether given elements of the group are standard generators.","abstract_has_math":false,"creators":["Nickerson, Simon Jon"],"institution":"University of Birmingham","degree_name":"d_ph","degree_level":"d_ph","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-07","date_published":"2006-07","updated_at":"2026-07-24T01:11:33Z","subjects":["QA Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.sponsor","label":"Sponsor","values":["epsrc"]},{"key":"dc:creator","label":"Author","values":["Nickerson, Simon Jon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2006-07-11"]},{"key":"dc:date.issued","label":"Date","values":["2006-07"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics & Statistics","School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Birmingham"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["http://etheses.bham.ac.uk//id/eprint/1463/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["d_ph"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["d_ph"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://etheses.bham.ac.uk//id/eprint/1463/1/Nickerson06PhD.pdf","http://etheses.bham.ac.uk//id/eprint/1463/2/Decl_IS_Nickerson06PhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Motivated by the World Wide Web Atlas of Finite Group Representations and the recent classification of low-dimensional representations of quasisimple groups in cross-characteristic fields by Hiss and Malle, we construct with a computer over 650 representations of finite simple groups. Explicit matrices for these representations are available on the Internet and are included on an attached CD-ROM. Our main tool is a GAP program for decomposing permutation modules. It uses reduction modulo various primes and rational reconstruction to give an acceptable performance. In addition, we define standard generators for the groups under consideration, and exhibit black box algorithms for finding standard generators and checking whether given elements of the group are standard generators."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["An atlas of characteristic zero representations"]}]}],"canonical_facts":{"dc:contributor.sponsor":["epsrc"],"dc:creator":["Nickerson, Simon Jon"],"dc:date":["2006-07-11"],"dc:date.issued":["2006-07"],"dc:description.abstract":["Motivated by the World Wide Web Atlas of Finite Group Representations and the recent classification of low-dimensional representations of quasisimple groups in cross-characteristic fields by Hiss and Malle, we construct with a computer over 650 representations of finite simple groups. Explicit matrices for these representations are available on the Internet and are included on an attached CD-ROM. Our main tool is a GAP program for decomposing permutation modules. It uses reduction modulo various primes and rational reconstruction to give an acceptable performance. 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