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We also give an example which shows that even for elementary amenable groups, it is not sufficient for biorderablity that the group be a residually finite p-group and a residually finite q-group.","abstract_html":"Let p and q be distinct primes, and G an elementary amenable group that is a residually finite p-group and a residually finite q-group. We conjecture that such groups G are left orderable. In this paper we show some results which came as attempts to prove this conjecture. In particular we give a condition under which split extensions of residually finite p-groups are again residually finite p-groups. We also give an example which shows that even for elementary amenable groups, it is not sufficient for biorderablity that the group be a residually finite p-group and a residually finite q-group.","abstract_has_math":false,"creators":["Withrow, Camron Michael"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Linnell, Peter A."],"committee_members":["Ball, Joseph A.","Brown, Ezra A."],"year":2014,"date_issued":"2014-01-03","date_published":"2014-01-03","updated_at":"2026-07-22T22:20:03Z","subjects":["left orderable group","residually finite p-group"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:2150"],"render_values":[{"text":"vt_gsexam:2150","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/24782","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Linnell, Peter A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ball, Joseph A.","Brown, Ezra A."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Withrow, Camron Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-01-04T09:00:07Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-01-04T09:00:07Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-01-03"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["left orderable group","residually finite p-group"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:2150"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/24782"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let p and q be distinct primes, and G an elementary amenable group that is a residually finite p-group and a residually finite q-group. We conjecture that such groups G are left orderable. In this paper we show some results which came as attempts to prove this conjecture. In particular we give a condition under which split extensions of residually finite p-groups are again residually finite p-groups. We also give an example which shows that even for elementary amenable groups, it is not sufficient for biorderablity that the group be a residually finite p-group and a residually finite q-group."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Left Orderable Residually Finite p-groups"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Linnell, Peter A."],"dc:contributor.committeemember":["Ball, Joseph A.","Brown, Ezra A."],"dc:contributor.department":["Mathematics"],"dc:creator":["Withrow, Camron Michael"],"dc:date.accessioned":["2014-01-04T09:00:07Z"],"dc:date.available":["2014-01-04T09:00:07Z"],"dc:date.issued":["2014-01-03"],"dc:description.abstract":["Let p and q be distinct primes, and G an elementary amenable group that is a residually finite p-group and a residually finite q-group. We conjecture that such groups G are left orderable. In this paper we show some results which came as attempts to prove this conjecture. In particular we give a condition under which split extensions of residually finite p-groups are again residually finite p-groups. We also give an example which shows that even for elementary amenable groups, it is not sufficient for biorderablity that the group be a residually finite p-group and a residually finite q-group."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:2150"],"dc:identifier.uri":["http://hdl.handle.net/10919/24782"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["left orderable group","residually finite p-group"],"dc:title":["Left Orderable Residually Finite p-groups"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:03Z"}