{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:54:58Z","timestamp":1776722098564,"version":"3.51.2"},"reference-count":7,"publisher":"American Mathematical Society (AMS)","issue":"218","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We present an algorithm to compute a full set of irreducible representations of a supersolvable group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G\">\n                        <mml:semantics>\n                          <mml:mi>G<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">G<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    over a finite field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper K\">\n                        <mml:semantics>\n                          <mml:mi>K<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"c h a r upper K does-not-divide StartAbsoluteValue upper G EndAbsoluteValue\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>char<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mi>K<\/mml:mi>\n                            <mml:mo>\n                              \u2224\n                              \n                            <\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\operatorname {char} K\\nmid |G|<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , which is not assumed to be a splitting field of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G\">\n                        <mml:semantics>\n                          <mml:mi>G<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">G<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The main subroutines of our algorithm are a modification of the algorithm of Baum and Clausen (Math. Comp.\n                    <bold>63<\/bold>\n                    (1994), 351\u2013359) to obtain information on algebraically conjugate representations, and an effective version of Speiser\u2019s generalization of Hilbert\u2019s Theorem\u00a090 stating that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript 1 Baseline left-parenthesis upper G a l left-parenthesis upper L slash upper K right-parenthesis comma upper G upper L left-parenthesis n comma upper L right-parenthesis right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>H<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>Gal<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>K<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>GL<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H^{1}(\\operatorname {Gal}(L\/K), \\operatorname {GL}(n,L))<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    vanishes for all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n greater-than-or-equal-to 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n\\ge 1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-97-00839-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"779-786","source":"Crossref","is-referenced-by-count":2,"title":["Computing irreducible representations of supersolvable groups over small finite fields"],"prefix":"10.1090","volume":"66","author":[{"given":"A.","family":"Omrani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Shokrollahi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[1997]]},"reference":[{"issue":"207","key":"1","doi-asserted-by":"publisher","first-page":"351","DOI":"10.2307\/2153580","article-title":"Computing irreducible representations of supersolvable groups","volume":"63","author":"Baum, Ulrich","year":"1994","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2","isbn-type":"print","volume-title":"Fast Fourier transforms","author":"Clausen, Michael","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3411163615"},{"key":"3","series-title":"Die Grundlehren der mathematischen Wissenschaften, Band 134","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-64981-3","volume-title":"Endliche Gruppen. I","author":"Huppert, B.","year":"1967"},{"key":"4","series-title":"Grundlehren der Mathematischen Wissenschaften","isbn-type":"print","volume-title":"Finite groups. II","volume":"242","author":"Huppert, Bertram","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/3540106324"},{"key":"5","unstructured":"M. Sch\u00f6nert et al., GAP \u2013 Groups, Algorithms, and Programming, Lehrstuhl D f\u00fcr Mathematik, Rheinisch Westf\u00e4lische Technische Hochschule, Aachen, Germany, fourth edition, 1994."},{"key":"6","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-5673-9","volume-title":"Local fields","volume":"67","author":"Serre, Jean-Pierre","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0387904247"},{"key":"7","doi-asserted-by":"crossref","unstructured":"A. Speiser, Zahlentheoretische S\u00e4tze aus der Gruppentheorie, Math. Zeit. 5 (1919), 1\u20136.","DOI":"10.1007\/BF01203150"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00839-9\/S0025-5718-97-00839-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00839-9\/S0025-5718-97-00839-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:27:25Z","timestamp":1776720445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00839-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"references-count":7,"journal-issue":{"issue":"218","published-print":{"date-parts":[[1997,4]]}},"alternative-id":["S0025-5718-97-00839-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-97-00839-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1997]]}}}