Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>
Presenting an explicit descryption of unit group in the integral group ring of a given non-abelian group is a classical and open problem. Let S3C3ℤ(S3×C3)(F55⋊F3)⋊(S3∗×C2)Fρρℤ(S3×C3)S3RS3R=ℤ[ω]ωℤ(G×C3)GV(G)GU(ℤ(G×C3))
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| Format: | Article |
| Language: | English |
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Miskolc University Press
2024-01-01
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| Series: | Miskolc Mathematical Notes |
| Online Access: | http://mat76.mat.uni-miskolc.hu/mnotes/article/4666 |
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| _version_ | 1832592247712907264 |
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| author | Ömer Küsmüş |
| author_facet | Ömer Küsmüş |
| author_sort | Ömer Küsmüş |
| collection | DOAJ |
| description | Presenting an explicit descryption of unit group in the integral group ring of a given non-abelian group is a classical and open problem. Let S3C3ℤ(S3×C3)(F55⋊F3)⋊(S3∗×C2)Fρρℤ(S3×C3)S3RS3R=ℤ[ω]ωℤ(G×C3)GV(G)GU(ℤ(G×C3)) |
| format | Article |
| id | doaj-art-d3941b563cbc41269c5ae0f3edaef1d7 |
| institution | Kabale University |
| issn | 1787-2405 1787-2413 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Miskolc University Press |
| record_format | Article |
| series | Miskolc Mathematical Notes |
| spelling | doaj-art-d3941b563cbc41269c5ae0f3edaef1d72025-01-21T12:00:07ZengMiskolc University PressMiskolc Mathematical Notes1787-24051787-24132024-01-0125284510.18514/MMN.2024.4666Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>Ömer KüsmüşPresenting an explicit descryption of unit group in the integral group ring of a given non-abelian group is a classical and open problem. Let S3C3ℤ(S3×C3)(F55⋊F3)⋊(S3∗×C2)Fρρℤ(S3×C3)S3RS3R=ℤ[ω]ωℤ(G×C3)GV(G)GU(ℤ(G×C3))http://mat76.mat.uni-miskolc.hu/mnotes/article/4666 |
| spellingShingle | Ömer Küsmüş Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math> Miskolc Mathematical Notes |
| title | Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math> |
| title_full | Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math> |
| title_fullStr | Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math> |
| title_full_unstemmed | Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math> |
| title_short | Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math> |
| title_sort | unit group of integral group ring mml math display inline mml mrow mml mi z mml mi mml mo class mathclass open mml mo mml mi g mml mi mml mo class mathclass bin mml mo mml msub mml mrow mml mi c mml mi mml mrow mml mrow mml mn 3 mml mn mml mrow mml msub mml mo class mathclass close mml mo mml mrow mml math |
| url | http://mat76.mat.uni-miskolc.hu/mnotes/article/4666 |
| work_keys_str_mv | AT omerkusmus unitgroupofintegralgroupringmmlmathdisplayinlinemmlmrowmmlmizmmlmimmlmoclassmathclassopenmmlmommlmigmmlmimmlmoclassmathclassbinmmlmommlmsubmmlmrowmmlmicmmlmimmlmrowmmlmrowmmlmn3mmlmnmmlmrowmmlmsubmmlmoclassmathclassclosemmlmommlmrowmmlmath |