Maximal Solvable Subgroups of Finite Classical Groups
Korhonen, Mikko
- 出版商: Springer
- 出版日期: 2024-07-27
- 售價: $2,830
- 貴賓價: 9.5 折 $2,689
- 語言: 英文
- 頁數: 300
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031629140
- ISBN-13: 9783031629143
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商品描述
This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields.
A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan's Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan's classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups.
The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan's work.
商品描述(中文翻譯)
本書研究有限域上古典群的極大可解子群。它提供了對Camille Jordan的古典結果的第一個現代解釋,並將其擴展,給出了一個對一般線性群、輔射群和正交群的極大不可約可解子群的分類,這些群可以是任意有限域上的。
群G的一個子群被稱為極大可解子群,如果它在可解子群中是極大的。這個概念的歷史可以追溯到Jordan的《Traité》(1870年),在這本書中,他對對稱群的極大可解子群進行了分類。主要困難在於原始情況,這導致了對素數次序域上的一般線性群的極大不可約可解子群進行分類的問題。本專著的一個目的是闡述:用現代術語證明Jordan的分類。更一般地,目標是將這些結果推廣到任意有限域上的古典群,並提供與不可約可解矩陣群相關的其他有趣結果。
本書對於對原始置換群、不可約矩陣群和相關的群論和表示論主題感興趣的研究生和研究人員是可理解的。詳細的介紹將吸引那些對Jordan的工作的歷史背景感興趣的讀者。
作者簡介
Mikko Korhonen is a research assistant professor at the Southern University of Science and Technology, Shenzhen, China. His main research interests are in topics related to the representation theory and subgroup structure of linear algebraic groups and finite groups. Previously, he was a postdoctoral research fellow at the University of Manchester, and he obtained his PhD from the École Polytechnique Fédérale de Lausanne.
作者簡介(中文翻譯)
Mikko Korhonen是中國深圳南方科技大學的研究助理教授。他的主要研究興趣涉及線性代數群和有限群的表示理論和子群結構等相關主題。在此之前,他曾在曼徹斯特大學擔任博士後研究員,並在洛桑聯邦理工學院獲得博士學位。