Book ChapterDOI
Finite Group Theory
Alexander Lubotzky,Dan Segal +1 more
- pp 319-327
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In this window, all groups are assumed finite as discussed by the authors, and a number of results of an elementary nature that we sometimes take for granted is easily available in textbooks such as [H], [R] and [A]).Abstract:
In this window, all groups are assumed finite. Here we collect a number of results that play a significant role in the book (further material of an elementary nature that we sometimes take for granted is easily available in textbooks such as [H], [R] and [A]).read more
Citations
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Journal ArticleDOI
Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
Igor P. Ivanov,Evgeny Vdovin +1 more
TL;DR: In this paper, the authors proposed a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM).
Book
Blocks of Finite Groups and Their Invariants
TL;DR: This paper presents a meta-anatomy of the determinants of infectious disease in eight operation rooms of the immune system and some of the mechanisms involved are described.
Journal ArticleDOI
Construction of 2-local finite groups of a type studied by Solomon and Benson
Ran Levi,Bob Oliver +1 more
TL;DR: In this article, the authors constructed a family of 2{local nite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2{subgroup of Spin7(q )( qan odd prime power) shown by Solomon not to occur as the 2{fusion in any actual nite group.
Journal ArticleDOI
On finitely generated profinite groups, II: products in quasisimple groups
Nikolay Nikolov,Dan Segal +1 more
TL;DR: In this article, it was shown that there is an absolute constant D such that for any finite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D twisted commutators defined by the given automomorphisms.
Posted Content
Product decompositions of quasirandom groups and a Jordan type theorem
Nikolay Nikolov,László Pyber +1 more
TL;DR: In this article, it was shown that if k is the minimal degree of a representation of the finite group G, then G has a proper subgroup of index at most ck^2 for some absolute constant c, hence a product-free subset of size at least $|G| / c'k.
References
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Book
Blocks of Finite Groups and Their Invariants
TL;DR: This paper presents a meta-anatomy of the determinants of infectious disease in eight operation rooms of the immune system and some of the mechanisms involved are described.
Journal ArticleDOI
Construction of 2-local finite groups of a type studied by Solomon and Benson
Ran Levi,Bob Oliver +1 more
TL;DR: In this article, the authors constructed a family of 2{local nite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2{subgroup of Spin7(q )( qan odd prime power) shown by Solomon not to occur as the 2{fusion in any actual nite group.
Posted Content
The classification of torsion endo-trivial modules
Jon F. Carlson,Jacques Thévenaz +1 more
TL;DR: In this paper, a major step in the classification of endo-trivial modules over p-groups is made. But the main result of this paper is that this group is torsion free except in the case that G is cyclic, quaternion or semi-dihedral.
Patching and Galois Theory
TL;DR: Galois theory over (x) is well-understood as a consequence of Riemann's Existence Theorem, which classifies the algebraic branched covers of the complex projective line as mentioned in this paper.
Journal ArticleDOI
Generators and commutators in finite groups; abstract quotients of compact groups
Nikolay Nikolov,Dan Segal +1 more
TL;DR: In this paper it was shown that a compact group cannot have a finitely generated infinite abstract quotient, and the results were applied to the study of normal subgroups in finite groups and in more general compact groups.