{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:55:10Z","timestamp":1776840910091,"version":"3.51.2"},"reference-count":3,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,3,8]],"date-time":"2006-03-08T00:00:00Z","timestamp":1141776000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We present an algorithm that computes the structure of a finite abelian 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                    from a generating system\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper M\">\n                        <mml:semantics>\n                          <mml:mi>M<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">M<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The algorithm executes\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper O left-parenthesis StartAbsoluteValue upper M EndAbsoluteValue StartRoot StartAbsoluteValue upper G EndAbsoluteValue EndRoot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">O<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>M<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:msqrt>\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:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\operatorname {O}(|M|\\sqrt {|G|})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    group operations and stores\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper O left-parenthesis StartRoot StartAbsoluteValue upper G EndAbsoluteValue EndRoot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">O<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msqrt>\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:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\operatorname {O}(\\sqrt {|G|})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    group elements.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01740-0","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"2017-2026","source":"Crossref","is-referenced-by-count":18,"title":["Computing the structure of a finite abelian group"],"prefix":"10.1090","volume":"74","author":[{"given":"Johannes","family":"Buchmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arthur","family":"Schmidt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2005,3,8]]},"reference":[{"issue":"220","key":"1","doi-asserted-by":"publisher","first-page":"1663","DOI":"10.1090\/S0025-5718-97-00880-6","article-title":"On some computational problems in finite abelian groups","volume":"66","author":"Buchmann, Johannes","year":"1997","journal-title":"Math. 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Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01740-0\/S0025-5718-05-01740-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01740-0\/S0025-5718-05-01740-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:31:02Z","timestamp":1776781862000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01740-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,8]]},"references-count":3,"journal-issue":{"issue":"252","published-print":{"date-parts":[[2005,10]]}},"alternative-id":["S0025-5718-05-01740-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-05-01740-0","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":[[2005,3,8]]}}}