1996 Fiscal Year Final Research Report Summary
Classification of ideals in integral group rings
| Project/Area Number |
06640035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Aichi University of Education |
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Principal Investigator |
TAHARA Kenichi Aichi Univ.Educ.Math.Sci.Prof., 教育学部・総合科学課程, 教授 (00024026)
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| Project Period (FY) |
1994 – 1996
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| Keywords | Augmentation ideal / Dimension subgroup problem / General Fox subgroups / Generalized dimension subgroup problem |
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| Research Abstract |
We will get a almost complete solution for long standing "dimension subgroup priblem" in integral group rings, and so we propose two methods extending the dimension subgroup problem.
1) identification of subgroups G* (1+DELTA^n (G) DELTA (H)) for any n*1
2) identification of subgroups G* (1+DELTA^n (G) +DELTA (G) DELTA (H)) for any n*1
For these problems we could identify the following subgroups
3) G* (1+DELTA^3 (G) +DELTA (G) DELTA (H))
4) G* (1+DELTA (H) DELTA (G) DELTA (H) +DELTA([H,G]) DELTA (H))
5) G* (1+DELTA^2 (G) DELTA (H) +DELTA (K) DELTA (H)) for some subgroup K determined by H.
On the other hand, when G/H is elementary abelian p-group, and any n, we could get a upper bound for the following subgroup G* (1+DELTA^n (G) DELTA (H) * U (n) V (n) H' where U (n), and V (n) are subgroups determined by H.
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