[PDF] On The Spread Of Classical Groups eBook

Author : Scott Harper
Publisher : Springer Nature
Page : 154 pages
File Size : 35,36 MB
Release : 2021-05-25
Category : Mathematics
ISBN : 3030741001

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This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.

Author : Alexander Hahn
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 35,94 MB
Release : 1989
Category : Mathematics
ISBN : 082185089X

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During his lifetime, L. K. Hua played a leading role in and exerted a great influence upon the development in China of modern mathematics, both pure and applied. His mathematical career began in 1931 at Tsinghua University where he continued as a professor for many years. Hua made many significant contributions to number theory, algebra, geometry, complex analysis, numerical analysis, and operations research. In particular, he initiated the study of classical groups in China and developed new matrix methods which, as applied by him as well as his followers, were instrumental in the successful attack of many problems. To honor his memory, a joint China-U.S. conference on Classical Groups and Related Topics was held at Tsinghua University in Beijing in May 1987. This volume represents the proceedings of that conference and contains both survey articles and research papers focusing on classical groups and closely related topics.

Author : Timothy C. Burness
Publisher : Cambridge University Press
Page : 365 pages
File Size : 26,40 MB
Release : 2016-01-15
Category : Mathematics
ISBN : 1107629446

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A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.

Author : Hermann Weyl
Publisher : Princeton University Press
Page : 336 pages
File Size : 20,28 MB
Release : 2016-06-02
Category : Mathematics
ISBN : 1400883903

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In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful." Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.

Author : C. M. Campbell
Publisher : Cambridge University Press
Page : 510 pages
File Size : 23,93 MB
Release : 2019-04-11
Category : Mathematics
ISBN : 110872874X

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These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.

Author : John Boardman
Publisher : Princeton University Press
Page : 352 pages
File Size : 38,98 MB
Release : 2023-08-15
Category : Art
ISBN : 0691252831

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From one of the world’s leading authorities on ancient Greek art, a groundbreaking account of how Greek images were understood and used by other ancient peoples, from Britain to China In this book, acclaimed archaeologist and art historian John Boardman explores Greek art as a foreign art transmitted to the non-Greeks of antiquity—peoples who weren’t necessarily able to judge the meaning of Greek art and who may have regarded the Greeks themselves with great hostility. Boardman examines how and why the arts of the classical world traveled and to what effect, from Britain to China, from roughly the eighth century BCE to the early centuries CE. In some places, such as Italy, Greek images were overwhelmingly successful. In Egypt, the Celtic world, the eastern steppes, and other regions with strong local traditions, they were never effectively assimilated. And in cultures where there was a subtler blend of influences, notably in the Buddhist east, classical images served as a catalyst to the generation of new styles. Along the way, Boardman demonstrates that looking at Greek art from the outside provides a wealth of new insights into Greek art itself, and he raises important questions about how images in general are copied and reinterpreted.

Author : Peter B. Kleidman
Publisher : Cambridge University Press
Page : 317 pages
File Size : 35,40 MB
Release : 1990-04-26
Category : Mathematics
ISBN : 052135949X

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With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

Author : Laurent Bartholdi
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 49,76 MB
Release : 2006-03-28
Category : Mathematics
ISBN : 3764374470

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This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.