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Character theory of finite groups
TLDR
The Schur index Projective representations Character degrees Character correspondence Linear groups Changing the characteristic Some character tables Bibliographic notes References Index as discussed by the authors The Schur Index Projective representation of charactersAbstract:
Algebras, modules, and representations Group representations and characters Characters and integrality Products of characters Induced characters Normal subgroups T.I. sets and exceptional characters Brauer's theorem Changing the field The Schur index Projective representations Character degrees Character correspondence Linear groups Changing the characteristic Some character tables Bibliographic notes References Index.read more
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Spectra of graphs
TL;DR: This book gives an elementary treatment of the basic material about graph Spectra, both for ordinary, and Laplace and Seidel spectra, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.
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The Classification of the Finite Simple Groups
TL;DR: In this article, the authors introduce the special odd case General lemmas Theorem (C^*_2$): Stage 1 Theorem $C^*) 2$: Stages 2 and 3 IV$_K$: Preliminary properties of $K$-groups Background references Expository references Glossary Index
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Advanced Modern Algebra
TL;DR: The first edition of the first year of graduate algebra course as mentioned in this paper was designed as a text for the course, but it can also serve as a reference since it contains more advanced topics as well.
Book ChapterDOI
A machine-checked proof of the odd order theorem
Georges Gonthier,Andrea Asperti,Jeremy Avigad,Yves Bertot,Cyril Cohen,François Garillot,Stéphane Le Roux,Assia Mahboubi,Russell O'Connor,Sidi Ould Biha,Ioana Pasca,Laurence Rideau,Alexey Solovyev,Enrico Tassi,Laurent Théry +14 more
TL;DR: This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant, using a comprehensive set of reusable libraries of formalized mathematics.
Journal ArticleDOI
Evenly distributed unitaries: On the structure of unitary designs
TL;DR: In this article, the authors present a necessary and sufficient criterion for deciding if a set of matrices constitutes a unitary t-design, i.e., the average of any tth order polynomial over the design equals the average over the entire unitary group.