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Book ChapterDOI

Finite Group Theory

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TLDR
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]).

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Citations
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Journal ArticleDOI

Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model

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

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

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.
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Product decompositions of quasirandom groups and a Jordan type theorem

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

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

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

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.