Conjugacy in Finite Classical Groups
暫譯: 有限古典群中的共軛性
de Franceschi, Giovanni, Liebeck, Martin W., O'Brien, Eamonn A.
相關主題
商品描述
This book provides a comprehensive coverage of the theory of conjugacy in finite classical groups. Given such a classical group G, the three fundamental problems considered are the following: to list a representative for each conjugacy class of G; to describe the centralizer of each representative, by giving its group structure and a generating set; and to solve the conjugacy problem in G--namely, given two elements of G, establish whether they are conjugate, and if so, find a conjugating element. The book presents comprehensive theoretical solutions to all three problems, and uses these solutions to formulate practical algorithms. In parallel to the theoretical work, implementations of these algorithms have been developed in Magma. These form a critical component of various general algorithms in computational group theory--for example, computing character tables and solving conjugacy problems in arbitrary finite groups.
商品描述(中文翻譯)
本書全面涵蓋了有限古典群中共軛理論的內容。針對這樣的古典群 G，考慮的三個基本問題如下：列出 G 的每個共軛類的代表；描述每個代表的中心化子，提供其群結構和生成集；以及解決 G 中的共軛問題——即給定 G 的兩個元素，確定它們是否共軛，如果是，則找到一個共軛元素。本書對這三個問題提供了全面的理論解決方案，並利用這些解決方案制定實用的算法。與理論工作並行，這些算法的實現已在 Magma 中開發。這些實現構成了計算群論中各種通用算法的關鍵組成部分——例如，計算角色表和解決任意有限群中的共軛問題。
作者簡介
Giovanni De Franceschi currently works as a software developer in Verona. He completed a PhD in mathematics at the University of Auckland in 2018; some of this work formed part of his PhD thesis. Martin W. Liebeck has been a professor at Imperial College London since 1991, and was Head of Pure Mathematics there between 1997 and 2024. He has published about 170 articles and books on finite and algebraic groups, representation theory, probabilistic group theory, and applications of these topics to areas such as model theory in logic, Markov theory in probability, combinatorics, and the design of algorithms in computational algebra. Liebeck is a Fellow of the American Mathematical Society, and was the recipient of the London Mathematical Society's Polya Prize in 2020. Eamonn A. O'Brien is a professor at the University of Auckland since 2006. His research interests are in group theory and computational algebra, with a particular focus on the development and implementation of effective algorithms and their application to solving related challenging problems. He has published about 100 research papers and is a coauthor of the "Handbook of Computational Group Theory." Many of his research outputs are incorporated into the leading computational algebra systems GAP and Magma. Elected a Fellow of the Royal Society of New Zealand in 2009 and awarded its 2020 Hector Medal, he is a recipient of a 2024 Humboldt Foundation Research Award.
作者簡介(中文翻譯)
喬凡尼·德·弗朗切斯基目前在維羅納擔任軟體開發人員。他於2018年在奧克蘭大學完成數學博士學位；他的部分研究成果成為了博士論文的一部分。 馬丁·W·利貝克自1991年以來一直是倫敦帝國學院的教授，並於1997年至2024年間擔任純數學系主任。他在有限群和代數群、表示理論、隨機群論及這些主題在邏輯模型理論、概率中的馬可夫理論、組合學以及計算代數中的演算法設計等領域的應用方面發表了約170篇文章和書籍。利貝克是美國數學學會的會士，並於2020年獲得倫敦數學學會的波利亞獎。 伊蒙·A·奧布萊恩自2006年以來是奧克蘭大學的教授。他的研究興趣集中在群論和計算代數，特別是有效演算法的開發和實施及其在解決相關挑戰性問題中的應用。他發表了約100篇研究論文，並共同編寫了《計算群論手冊》。他的許多研究成果被納入領先的計算代數系統GAP和Magma中。2009年當選為紐西蘭皇家學會會士，並於2020年獲得赫克托獎勳章，他還是2024年洪堡基金會研究獎的獲得者。
