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Representations of finite groups

1990
*
ChoiceReviews
*

Introduction A

doi:10.5860/choice.27-3345
fatcat:f4kyra5h5rdsvm3flrwitfbhh4
*representation*(π, V )*of*G on a*finite*-dimensional complex vector space V is a homomorphism π from the*group*G to the*group*GL(V )*of*invertible complex linear maps from V to itself. ... Because any*finite*abelian*group*is a product*of*cyclic*groups*, the*group*G * is always isomorphic to G, but not canonically. ... Let G be the 'Heisenberg'*group*in SL 3 (Z/p)*of*all unipotent matrices The center Z*of*this*group*is made up*of*the matrices with x = y = 0, hence isomorphic to Z/p. ...##
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Representations of finite groups
[article]

2006
*
arXiv
*
pre-print

This book is an introduction to a fast developing branch

arXiv:math/0612104v1
fatcat:pbzdulunsnfgbbusahgkbezfxm
*of*mathematics - the theory*of**representations**of**groups*. It presents classical results*of*this theory concerning*finite**groups*. ...*of*a*finite**group*G. ... As for the*finite*-dimensional*representations**of**finite**groups*, we have proved their equivalence to some unitary*representations*. § 3. Characters*of**group**representations*. ...##
###
Representations of finite groups
[chapter]

2010
*
Spaces of Constant Curvature
*

Introduction A

doi:10.1090/chel/372/04
fatcat:qp5qddceo5cydfl3nksqv3t7ha
*representation*(π, V )*of*G on a*finite*-dimensional complex vector space V is a homomorphism π from the*group*G to the*group*GL(V )*of*invertible complex linear maps from V to itself. ... Because any*finite*abelian*group*is a product*of*cyclic*groups*, the*group*G * is always isomorphic to G, but not canonically. ... Let G be the 'Heisenberg'*group*in SL 3 (Z/p)*of*all unipotent matrices The center Z*of*this*group*is made up*of*the matrices with x = y = 0, hence isomorphic to Z/p. ...##
###
Representations of Finite Groups
[chapter]

2019
*
Group Theory for Physicists
*

Typical structures amenable to

doi:10.1017/9781108554862.004
fatcat:tipbzfgwwfe33eqm5fa2zy6tla
*representation*theory are*groups*, associative algebras and Lie algebras. In this thesis we study linear*representations**of**finite**groups*. ...*Representation*theory is concerned with the ways*of*writing elements*of*abstract algebraic structures as linear transformations*of*vector spaces. ... Introduction*Representations**of**finite**groups*provide a way*of*describing an abstract*group*as a*group**of*matrices. We will only consider linear*representations*. ...##
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Representations of Finite Groups
[chapter]

1999
*
Lectures on Representation Theory
*

Because any

doi:10.1142/9789812815743_0002
fatcat:pk44aqwqxze47n3lozeiwlcopq
*finite*abelian*group*is a product*of*cyclic*groups*, the*group*G * is always isomorphic to G, but not canonically. ... Introduction A*representation*(π, V )*of*G on a*finite*-dimensional complex vector space V is a homomorphism π from the*group*G to the*group*GL(V )*of*invertible complex linear maps from V to itself. ... The classification*of*irreducible*representations**of*G is reduced, to some extent, to that*of*classifying those*of*the smaller*groups*H and H\G. ...##
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Graph representations of finite Abelian groups

1981
*
Czechoslovak Mathematical Journal
*

*of*

*finite*Abelian

*groups*. ... Let (^ be a non-trivial

*finite*Abelian

*group*which can be expressed as a direct product

*of*cyclic

*groups*

*of*pairwise different orders. Then the

*group*© has a directed graph

*representation*. Proof. ...

##
###
Homotopy representations of finite groups

1982
*
Publications mathématiques (Bures-sur-Yvette)
*

The proof

doi:10.1007/bf02700464
fatcat:26coqdtwvrgvjeqbzijdigg23a
*of*(10.17) is a consequence*of*the following lemmas. Lemma (10.18). -dimQV(G)^o) < i. ... TAMMOTOMDIECKANDTEDPETRIE Homotopy*representation**groups*The homotopy*representation**groups*now to be defined are the analogues*of*the*representation*ring. ... It is quite straightforward to show that v{G, X) is a*finite**group*using the degree function. We note that (o(X, X) is a ring for any homotopy*representation*X*of*G. ...##
###
Representation Theory of Finite Groups
[article]

2010
*
arXiv
*
pre-print

The point

arXiv:1001.0462v1
fatcat:vd3gybd36vbc3of5aasuzzclxy
*of*view*of*these notes on the topic is to bring out the flavor that*Representation*Theory is an extension*of*the first course on*Group*Theory. ... A large number*of*worked out examples are the main feature*of*these notes. The prerequisite for this note is basic*group*theory and linear algebra. ... CHAPTER 5*Representation*Theory*of**Finite*Abelian*Groups*over C Throughout this chapter G denotes a*finite*Abelian*group*. Proposition 5.1. Let k = C and G be a*finite*Abelian*group*. ...##
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Representations of Finite Polyadic Groups
[article]

2010
*
arXiv
*
pre-print

Using this correspondence, we generalize some well-known properties

arXiv:1011.0954v1
fatcat:ydpxvhykrvf6vc2dm7wmyrrwxu
*of*irreducible characters in*finite**groups*to the case*of*polyadic*groups*. ... We prove that there is a one-one correspondence between sets*of*irreducible*representations**of*a polyadic*group*and its Post's cover. ... Especially, the number*of*irreducible*representations**of*any*finite*polyadic*group*is*finite*. ...##
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Representations of locally finite groups

1968
*
Bulletin of the American Mathematical Society
*

The purpose

doi:10.1090/s0002-9904-1968-11913-5
fatcat:zrz4qlxwtvewxmyzqbjhm53lka
*of*this paper is to give a brief general account*of*the completely reducible*finite*-dimensional*representations**of*a locally*finite**group*G over a given algebraically closed field K. ... If G is*finite*, the assertion follows (upon passing to the*group*algebra*of*G over F) from the fact that if A is a*finite*-dimensional associa* tive algebra over F, then an irreducible (*finite*-dimensional ...##
###
Tensor representation of finite groups

1972
*
Journal of combinatorial theory. Series A
*

Employing the tensor terminology introduced, a proof that the degrees

doi:10.1016/0097-3165(72)90082-9
fatcat:mszx37dwvzgdnlgaieq72wowbe
*of*the irreducible*representations**of*a*finite**group*divide the*group*order is given which is somewhat different from the usual proofs ... A cubic array*of*O's and l's, a 34mensional analog*of*the 2dimensional array*of*O's and l's defined by a permutation matrix, can be employed to represent a*finite**group*. ... The orthogonality relations for*group**representations*and*group*characters are*of*fundamental importance in the study*of**finite**groups*. ...##
###
Small Representations of Finite Classical Groups
[article]

2016
*
arXiv
*
pre-print

*Finite*

*group*theorists have established many formulas that express interesting properties

*of*a

*finite*

*group*in terms

*of*sums

*of*characters

*of*the

*group*. ... Despite the classification by Lusztig

*of*the irreducible

*representations*

*of*

*finite*

*groups*

*of*Lie type, it seems that this aspect remains obscure. ... Finally, S.G. thanks the UW-Madison for choosing him as a Vilas Associate for the period

*of*working on this project. ...

##
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On Abelian Group Representability of Finite Groups
[article]

2012
*
arXiv
*
pre-print

A set

arXiv:1212.1298v2
fatcat:pwwypthqk5gn7ev4p45zmi6x2y
*of*quasi-uniform random variables X_1,...,X_n may be generated from a*finite**group*G and n*of*its subgroups, with the corresponding entropic vector depending on the subgroup structure*of*G. ... It is known that the set*of*entropic vectors obtained by considering arbitrary*finite**groups*is much richer than the one provided just by abelian*groups*. ... abelian*Group**Representability**of*Nilpotent*Groups*A*finite*nilpotent*group*is a direct product*of*its Sylow p subgroups. ...##
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On Abelian group representability of finite groups

2014
*
Advances in Mathematics of Communications
*

A set

doi:10.3934/amc.2014.8.139
fatcat:ke5ovyi6m5habmwxinnmdynmnm
*of*quasi-uniform random variables X 1 , . ... abelian*Group**Representability**of*Nilpotent*Groups*A*finite*nilpotent*group*is a direct product*of*its Sylow p subgroups. ... The contributions*of*this paper are to introduce the notion*of*abelian*group**representability*for an arbitrary*finite**group*G, and to characterize the abelian*group**representability**of*several classes ...##
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Convergence and limits of linear representations of finite groups
[article]

2015
*
arXiv
*
pre-print

Motivated by the theory

arXiv:1406.5032v5
fatcat:sowcowk7enbhfghebw7u6dvq5a
*of*graph limits, we introduce and study the convergence and limits*of*linear*representations**of**finite**groups*over*finite*fields. ... The limit objects are infinite dimensional*representations**of*free*groups*in continuous algebras. We show that under a certain integrality condition, the algebras above are skew fields. ... By a*finite*dimensional unitary*representation*(*of*degree r), we mean a homomorphism κ : F r → U (n)*of*the free*group*on r generators into the unitary*group*U (n). ...
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