Generalized prime graphs and the structure of finite groups.
| Project/Area Number |
22540023
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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 | Yamaguchi University |
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Principal Investigator |
IIYORI Nobuo 山口大学, 教育学部, 教授 (00241779)
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| Project Period (FY) |
2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 有限群 / 単純群 / 素数グラフ / クイヴァ / 束 / ホモロジー / prime graph / バーンサイド環 / 部分群束 |
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| Research Abstract |
Let P be a group property and let G be a finite group. The generalized prime graph Γ of G associated with P, or simply theP-graph of G, is a graph whose vertex set is π(G). Two vertices p,q of Γare joined by an edge if and only if there exists a P-subgroup of G whose order is divisible by pq. There are deep relations between the structure of P-graphs and the one of P-subgroup lattices L(G,P) of G. In our research we study the structure of P-subgroup lattice (or group) from point of view of P-graphs. We define a new algebra UD(Q) for a quiver Q and we study UD(L(G,P)). We also find some relations between the structure of G and the one of UD(L(G,P)) and determine the structure of UD(Q) for some quiver Q completely.
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Report
(4 results)
Research Products
(5 results)
