| Project/Area Number |
17540009
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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 | Gunma University |
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Principal Investigator |
FUKUSHIMA Hiroshi Gunma University, Faculty of Education, Professor, 教育学部, 教授 (30125869)
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| Co-Investigator(Kenkyū-buntansha) |
NINOMIYA Yasushi Shinsyu University, Faculty of Science, Professor, 理学部, 教授 (40092887)
WADA Tomoyuki Tokyo University of Agriculture and Technology, Faculty of Technology, Professor, 工学部, 教授 (30134795)
OHTAKE Koichiro Gunma University, Faculty of Education, Professor, 教育学部, 教授 (60134269)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | irreducible product / module / character / solvable group / M-group |
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| Research Abstract |
A character of a finite group G is monomial if it is induced from a linear character of a subgroup of G. A group G is an M-group if all its complex irreducible character are monomial. Isaacs asked whether Hall subgroups of M-group need be M-groups. Concerning this problem, we gave examples of M-groups that have Hall subgroups that are not M-groups.
Next, Isaacs conjectured the following.
Conjecture. A solvable group having an irreducible character that factors as a product of two faithful characters is necessarily cyclic.
Concerning this problem, we proved the following theorem.
Theorem. Let G be an M-group and suppose that some irreducible character of G is a product of two faithful characters. Then G is cyclic.
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