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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 于靖(Jing Yu) | |
dc.contributor.author | Yu-Chung Liu | en |
dc.contributor.author | 劉又中 | zh_TW |
dc.date.accessioned | 2021-05-19T17:48:49Z | - |
dc.date.available | 2023-01-04 | |
dc.date.available | 2021-05-19T17:48:49Z | - |
dc.date.copyright | 2018-01-04 | |
dc.date.issued | 2017 | |
dc.date.submitted | 2017-11-21 | |
dc.identifier.citation | [BN41] R. Brauer and C. Nesbitt. On the modular characters of groups. Ann. of Math. (2), 42:556–590, 1941.
[Bre99] Thomas Breuer. Decomposition matrices, 1999. http://www.math.rwth-aachen.de/homes/MOC/decomposition/. [Bur76] R. Burkhardt. Die Zerlegungsmatrizen der Gruppen PSL(2, p^f). J. Algebra, 40(1):75–96, 1976. [CCN+85] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson. Atlas of finite groups. Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray. [CR90] Charles W. Curtis and Irving Reiner. Methods of representation theory. Vol. I. Wiley Classics Library. John Wiley & Sons, Inc., New York, 1990. With applications to finite groups and orders, Reprint of the 1981 original, A Wiley-Interscience Publication. [CR06] Charles W. Curtis and Irving Reiner. Representation theory of finite groups and associative algebras. AMS Chelsea Publishing, Providence, RI, 2006. Reprint of the 1962 original. [Dad66] E. C. Dade. Blocks with cyclic defect groups. Ann. of Math. (2), 84:20–48, 1966. [FH91] William Fulton and Joe Harris. Representation theory, volume 129 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1991. A first course, Readings in Mathematics. [Gre55] J. A. Green. The characters of the finite general linear groups. Trans. Amer. Math. Soc., 80:402–447, 1955. [JLPW95] Christoph Jansen, Klaus Lux, Richard Parker, and Robert Wilson. An atlas of Brauer characters, volume 11 of London Mathematical Society Monographs. New Series. The Clarendon Press, Oxford University Press, New York, 1995. Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications. [PD77] B. M. Puttaswamaiah and John D. Dixon. Modular representations of finite groups. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. Pure and Applied Mathematics, No. 73. [Ser77] Jean-Pierre Serre. Linear representations of finite groups. Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott, Graduate Texts in Mathematics, Vol. 42. [Ste51] Robert Steinberg. The representations of GL(3, q), GL(4, q), PGL(3, q), and PGL(4, q). Canadian J. Math., 3:225–235, 1951. [Web16] Peter Webb. A course in finite group representation theory, volume 161 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2016. [王13] 王義榮. An application of character tables of SL(3, q) and its subgroups. 國立成功大學應用數學研究所碩士論文, 2013. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7643 | - |
dc.description.abstract | 令 G 為一有限子群,p 為 |G| 的一個質因數,並令 G_p' := {g 屬於 G : g 的階 (order) 與 p 互質 }。如果 φ 是一個簡單 p-模特徵 (simple p-modular character),並且存在一個簡單複特徵 (simple complex character) χ 以及正整數 N,使得對於所有
G_p'中的元素 g,χ(g) = Nφ(g),則我們說 φ 具有幾乎可提性。上述情況中若 N = 1,則我們說 φ 具有可提性。 如果 G 的每個簡單 p-模特徵都具可提性,或至少存在一個 G 的簡單 p-模特徵不是幾乎可提的,則我們會說 G 具有 (L, p)-性質。而我們會說 G 具有 (L', p)-性質,如果 G 的每個複特徵 χ 都滿足以下命題:若存在正整數 N 以及 G 的簡單 p-模特徵 φ,使得 χ 限制在 G_p' 上時與 Nφ 相等,則 N = 1。 在本文中,我們會發現若 G 具有 (L', p)-性質,則 G 亦有 (L, p)-性質。並且我們會證明當 n ≦ 3 且 q > 1 為一質數的冪次時,對於任意質數 p,矩陣群 GL(n, q) 以及 SL(n, q) 皆有 (L', p)-性質。 | zh_TW |
dc.description.abstract | Let G be a finite group, and fix p a prime divisor of |G|. Denote G_p' as the set of p-regular elements of G. A simple p-modular character φ of G is said to be almost liftable if there exists a simple complex character χ of G such that χ = Nφ on G_p' for some positive integer N. Moreover if N = 1, φ is said to be liftable.
We say that G has the (L, p)-property if either there exists a simple p-modular character which is not almost liftable, or all the simple p-modular characters are liftable; and G is said to have the (L', p)-property if whenever χ is a simple complex character of G and χ = Nφ on G_p' for some simple p-modular character φ, then we have N = 1. In this thesis, we observe that the (L', p)-property of G implies the (L, p)-property of G, and show that when n = 2, 3, the general linear groups GL(n, q) and the special linear groups SL(n, q) have the (L', p)-property for any prime p and any prime power q. | en |
dc.description.provenance | Made available in DSpace on 2021-05-19T17:48:49Z (GMT). No. of bitstreams: 1 ntu-106-R02221022-1.pdf: 1449062 bytes, checksum: cbbcca22a24a88fb278f29b189e013c1 (MD5) Previous issue date: 2017 | en |
dc.description.tableofcontents | 口試委員會審定書 . . . i
致謝 . . . ii 中文摘要 . . . iii Abstract . . . iv 1 Introduction . . . 1 2 Preliminaries . . . 3 3 (L′, p)-Properties of Finite General Linear Groups and Special Linear Groups . . . 15 3.1 Basic Properties of GL(n, q) . . . 15 3.2 Simple Characters of GL(n, q) . . . 19 3.3 (L′, p)-Properties of GL(2, q), SL(2, q), GL(3, q), and SL(3, q) . . . 23 4 Other Methods for Proving (L, p)-Properties . . . 43 4.1 Degrees of Simple Modular Characters . . . 43 4.2 Decomposition Matrices . . . 46 References . . . 58 | |
dc.language.iso | en | |
dc.title | p-模特徵的可提性 | zh_TW |
dc.title | On Lifting of Modular Characters | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 潘戍衍(Shu-Yen Pan),林惠雯(Hui-Wen Lin),郭文堂(Wentang Kuo) | |
dc.subject.keyword | 模特徵,可提性,幾乎可提性,(L, p)-性質, | zh_TW |
dc.subject.keyword | modular character,liftable,almost liftable,(L, p)-property, | en |
dc.relation.page | 60 | |
dc.identifier.doi | 10.6342/NTU201704352 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2017-11-21 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
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