Normal 2-Coverings of the Finite Simple Groups and Their Generalizations
Bubboloni, Daniela, Spiga, Pablo, Weigel, Thomas Stefan
- 出版商: Springer
- 出版日期: 2024-07-23
- 售價: $2,840
- 貴賓價: 9.5 折 $2,698
- 語言: 英文
- 頁數: 180
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031623479
- ISBN-13: 9783031623479
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商品描述
This book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,
商品描述(中文翻譯)
本書提供了對非阿貝爾簡單群及其一般化的正常 2 覆蓋的完整且全面的分類。在為讀者提供對這些結構及其所包含群體的深入理解的同時，還探討了弱正常覆蓋的性質。重點是群體 G 的弱正常覆蓋數，即每個 G 的元素必須在這些子群中的一個內有共軛元素所需的最小適當子群數。這個數量對於每個非阿貝爾簡單群來說至少為 2，並且達到這一最小值的非阿貝爾簡單群被進行了分類。接下來的討論轉向幾乎簡單群，並對其弱正常覆蓋數提供了一些見解。應用範圍涵蓋代數數論、組合學、伽羅瓦理論等領域。本書彙編了現有的材料，並將其綜合成一個連貫的框架，對有限群論的這一基本方面提供了完整的概述。它將成為研究非阿貝爾簡單群的研究人員和研究生的重要資源。
作者簡介
Daniela Bubboloni is Professor of Mathematics at the University of Florence (Italy). Her main research interests involve finite groups and graph theory. A peculiar aspect of her research is the application of permutation groups and graph theory to questions of social choice theory, a branch of economics.
Pablo Spiga is Professor of Mathematics at the University of Milano-Bicocca (Italy). His main research interests involve group actions on graphs and other combinatorial structures. His main expertise is in finite primitive groups and their application to the investigation of symmetries of combinatorial structures.
Thomas Weigel is Professor of Mathematics at the University of Milano-Bicocca (Italy). His research interests are in the theory of groups, their representation theory and their cohomology theory. His main expertise is in the theory of groups of Lie-type, and the structure theory and cohomology of profinite groups.
作者簡介(中文翻譯)
丹妮拉·布布隆（Daniela Bubbolon）是佛羅倫斯大學（意大利）的數學教授。她的主要研究興趣包括有限群和圖論。她研究的一個特殊方面是將置換群和圖論應用於社會選擇理論的問題，這是一個經濟學的分支。
巴布羅·斯皮加（Pablo Spiga）是米蘭比科卡大學（意大利）的數學教授。他的主要研究興趣涉及群作用於圖和其他組合結構。他的主要專長是有限原始群及其在調查組合結構對稱性方面的應用。
托馬斯·維格爾（Thomas Weigel）是米蘭比科卡大學（意大利）的數學教授。他的研究興趣在於群的理論、它們的表示理論和同調理論。他的主要專長是李類型群的理論，以及完備群的結構理論和同調理論。
