{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:48:32Z","timestamp":1776721712762,"version":"3.51.2"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"213","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we compute the cohomology\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript asterisk Baseline left-parenthesis upper G semicolon upper Z Superscript w Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>H<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>Z<\/mml:mi>\n                              <mml:mi>w<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H^*(G;Z^w)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"w\">\n                        <mml:semantics>\n                          <mml:mi>w<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">w<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -basic 2-groups\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis upper G comma w right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>w<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(G,w)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with integral coefficients twisted by the orientation character\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"w\">\n                        <mml:semantics>\n                          <mml:mi>w<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">w<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We also calculate appropriate restiction maps and thus prove that the cohomology of any\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"w\">\n                        <mml:semantics>\n                          <mml:mi>w<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">w<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -basic group is detected by subgroups isomorphic to one of five types, and we provide a sample application of this main theorem.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00679-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"291-306","source":"Crossref","is-referenced-by-count":3,"title":["Integral cohomology and detection of \ud835\udc64-basic 2-groups"],"prefix":"10.1090","volume":"65","author":[{"given":"Kimberly","family":"Pearson","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"24","DOI":"10.2307\/1970305","article-title":"Torsion in \ud835\udc3b-spaces","volume":"74","author":"Browder, William","year":"1961","journal-title":"Ann. of Math. 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