{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:18:20Z","timestamp":1758709100077},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:p> Let [Formula: see text] be a finite group acting on a group [Formula: see text] as a group automorphisms, [Formula: see text] the bar complex, [Formula: see text] the homology of invariant group chains and [Formula: see text] the cohomology invariant, both defined in Knudson\u2019s paper \u201cThe homology of invariant group chains\u201d. In this paper, we define the Tate homology of invariants [Formula: see text] and the Tate cohomology of invariants [Formula: see text]. When the coefficient [Formula: see text] is the abelian group of the integers, we proved that these groups are isomorphics, [Formula: see text]. Further, we prove that the homology and cohomology of invariant group chains are duals, [Formula: see text], [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196721500156","type":"journal-article","created":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T10:29:40Z","timestamp":1604917780000},"page":"279-301","source":"Crossref","is-referenced-by-count":1,"title":["Tate (Co)homology of invariant group chains"],"prefix":"10.1142","volume":"31","author":[{"given":"Rolando","family":"Jimenez","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1ticas, Unidad Oaxaca, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Le\u00f3n 2, 68000 Oaxaca de Ju\u00e1rez, Oaxaca, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelina L\u00f3pez","family":"Madrigal","sequence":"additional","affiliation":[{"name":"Escuela de Ciencias, Universidad Aut\u00f3noma Benito Ju\u00e1rez de Oaxaca, Priv. 12 de Junio 100, 68125 Oaxaca de Ju\u00e1rez, Oaxaca, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,12,15]]},"reference":[{"key":"S0218196721500156BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9327-6"},{"key":"S0218196721500156BIB002","volume-title":"Abstract Algebra","author":"Dummit D. S.","year":"2004"},{"key":"S0218196721500156BIB003","doi-asserted-by":"publisher","DOI":"10.17323\/1609-4514-2018-18-1-149-162"},{"key":"S0218196721500156BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.01.044"},{"issue":"25","key":"S0218196721500156BIB005","first-page":"256","volume":"64","author":"Kunneth","year":"1975","journal-title":"Pure Appl. Math."},{"key":"S0218196721500156BIB006","volume-title":"Homology","author":"Lane S. Mac","year":"1965"},{"key":"S0218196721500156BIB007","volume-title":"Cohomology of Groups","author":"Weiss E.","year":"1969"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196721500156","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T09:23:13Z","timestamp":1618219393000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196721500156"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,15]]},"references-count":7,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1142\/S0218196721500156"],"URL":"https:\/\/doi.org\/10.1142\/s0218196721500156","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,15]]}}}