2013 Fiscal Year Final Research Report
Research on p-adic properties of the numbers of permutation representations
| Project/Area Number |
22540004
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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 | Muroran Institute of Technology |
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Principal Investigator |
TAKEGAHARA Yugen 室蘭工業大学, 工学(系)研究科(研究院), 教授 (10211351)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 準同型 / 対称群 / 交代群 / 環積 / p進的性質 |
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| Research Abstract |
There are three results. 1) p-adic properties of the number of homomorphisms from a finite abelian p-group to symmetric groups were obtained. In particular, the exponent of p of the decomposition of such numbers into prime factors was made clear. There are 6 different types of the results. 2) The exponent of 2 in the decomposition of one plus the number of involutions in alternating groups or wreath products of a cyclic group of order 2 by alternating groups groups into prime factors could be described as 2-adic integers. 3)p-adic properties of the number of homomorphisms from the direct product of two cyclic p-groups to wreath product of a cyclic p-group by symmetric groups were obtained. The results are closely related to that for the number of homomorphisms to symmetric groups.
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