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The model theory of unitriangular groups

1994
*
Annals of Pure and Applied Logic
*

*The*

*model*

*theory*

*of*

*groups*

*of*

*unitriangular*matrices over rings is studied. An important tool in these studies is a new notion

*of*a quasiunitriangular

*group*. ...

*The*

*models*

*of*

*the*

*theory*

*of*all

*unitriangular*

*groups*(

*of*fixed nilpotency class) are algebraically characterized; it turns out that all they are quasiunitriangular

*groups*. ... In Section 3 we study

*the*number

*of*

*models*in a power

*of*

*the*

*theory*

*of*a

*unitriangular*

*group*. ...

##
###
Page 5259 of Mathematical Reviews Vol. , Issue 2001H
[page]

2001
*
Mathematical Reviews
*

Part 2 treats

*the**model**theory**of**unitriangular**groups*. ... (RS-KEME; Kemerovo)*Model**theory**of**unitriangular**groups*.*Model**theory*and applications, 1-116, Amer. Math. Soc. Transl. Ser.2, 195, Amer. Math. Soc., Providence, RI, 1999. ...##
###
Page 6412 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

*The*final section

*of*

*the*paper treats

*the*number

*of*

*models*in a power

*of*

*the*

*theory*

*of*a

*unitriangular*

*group*. Many definitive results are obtained. ... (RS-KEME; Kemerovo)

*The*

*model*

*theory*

*of*

*unitriangular*

*groups*. (English summary) Ann. Pure Appl. Logic 68 (1994), no. 3, 225-261. ...

##
###
Quasiunitriangular groups

1993
*
Journal of Symbolic Logic (JSL)
*

For a ring with unit R, which need not be associative, denote

doi:10.2307/2275333
fatcat:gpy4zta4ifcxjdcziendf2f2ce
*the**group**of*upper*unitriangular*3 × 3 matrices over R by UT3(R). ... Mal′cev [M] gave an algebraic characterization*of**the*expanded*groups**of**the*form (R) as follows. ... Belegradek, "Some open problems in*the**model**theory**of**unitriangular**groups*", Proceedings*of**the*10th Easter Conference on*Model**Theory*, Humboldt Univ., Berlin, 1993, 9-13 Zentralblatt MATH [16] ...##
###
On computable subgroups of the group of all unitriangular matrices over a ring

2017
*
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
*

*Groups*

*of*

*unitriangular*matrices over

*the*ring are a classic representative

*of*

*the*class

*of*nilpotent

*groups*and have numerous applications both in

*group*

*theory*and in its applications. ... On computable subgroups

*of*

*the*

*group*

*of*all

*unitriangular*matrices over a ring

*The*problems

*of*existence and uniqueness

*of*computable numberings are fundamental in

*theory*

*of*computably numbered

*groups*. ... Our basic references for

*models*,

*groups*and rings are respectively [5] [6] [7] ,

*of*which we adopt terminology and notations. ...

##
###
Hopf monoids from class functions on unitriangular matrices

2013
*
Algebra & Number Theory
*

We build, from

doi:10.2140/ant.2013.7.1743
fatcat:ddv75cute5hzvewinu4wnsavwy
*the*collection*of*all*groups**of**unitriangular*matrices, Hopf monoids in Joyal's category*of*species. ... Superclasses*of**unitriangular*matrices admit a simple description from which we deduce a combinatorial*model*for*the*Hopf monoid*of*superclass functions, in terms*of**the*Hadamard product*of**the*Hopf monoids ... Acknowledgements We thank*the*referee and Franco Saliola for useful comments and suggestions. ...##
###
The polytabloid basis expands positively into the web basis
[article]

2018
*
arXiv
*
pre-print

We show that

arXiv:1808.00445v1
fatcat:unplvu6k2bhyxatwmmin456rhe
*the*transition matrix from*the*polytabloid basis to*the*web basis*of**the*irreducible S_2n-representation*of*shape (n,n) has nonnegative integer entries. ... This proves a conjecture*of*Russell and Tymoczko. ...*The*module W n is irreducible*of*shape (n, n) (see [5] );*the*basis {w M : M ∈ W n } is*the*web basis*of*W n .*The*web basis is related to*the*invariant*theory**of**the*Lie*group*SL 2 . ...##
###
THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS

2019
*
Forum of Mathematics, Sigma
*

We show that

doi:10.1017/fms.2019.22
fatcat:f2q73h2nmbghrdrqfepy2lfvdq
*the*transition matrix from*the*polytabloid basis to*the*web basis*of**the*irreducible $\mathfrak{S}_{2n}$ -representation*of*shape $(n,n)$ has nonnegative integer entries. ... This proves a conjecture*of*Russell and Tymoczko [Int. Math. Res. Not., 2019(5) (2019), 1479–1502]. ...*The*author thanks an anonymous referee for their careful reading*of*this manuscript and numerous helpful suggestions for improving*the*exposition. ...##
###
Page 6174 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

*Unitriangular*

*groups*and undecidability. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1993, no. 3, 19-22.

*The*paper contains some strengthenings

*of*

*the*author’s earlier results. ... Here UT,,(R) denotes

*the*

*group*

*of*all upper

*unitriangular*n x n matrices over R. (2) For any Turing degrees d; and d> such that d, < d> there exists a ring R such that for any n > 3, Th(UT,,(R)) has degree ...

##
###
Page 1473 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

Then, via suitable interpretations, he shows that #(7) coincides with PC when T is

*the**theory**of**the*ring*of*integers,*the**theory**of**the*field*of*rational numbers, or*the**theory**of**the**group**of*3 x 3*unitriangular*... As a corollary, it follows that #(T) = PC when T is*the**theory**of*rings,*the**theory**of*fields, or*the**theory**of**groups*. ...##
###
Page 01 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

Belegradek, Some open problems in

*the**model**theory**of**unitriangular**groups*(9-13); Sakaé Fuchino, Some problems*of*Séepin on openly generated Boolean algebras (14-29); D. ... In this very personal paper,*the*author gives his perspective on*the*development*of*set*theory*and*model**theory*, and discusses some*of*his main sources*of*motivation. ...##
###
A short proof on the transition matrix from the Specht basis to the Kazhdan-Lusztig basis
[article]

2019
*
arXiv
*
pre-print

We provide a short proof on

arXiv:1912.03809v1
fatcat:md7i5gbtcfgq3ieqapbmgh3tre
*the*change-*of*-basis coefficients from*the*Specht basis to*the*Kazhdan-Lusztig basis, using Kazhdan-Lusztig*theory*for parabolic Hecke algebra. ... M.S.I. was partially supported by*the*Summer Collaborators Program at*the*School*of*Mathematics in*the*Institute for Advanced Study in Princeton, NJ. ...*The*author would like to thank Chun-Ju Lai, Arik Wilbert, and Jieru Zhu for insightful discussions. ...##
###
Page 5284 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Belegradek,

*Model**theory**of**unitriangular**groups*(1-116); O. V. Belegradek,*Model**theory**of*locally free alge- bras [MR_ 89i:03056] (117-143); A. A. ... Kudaibergenov,*The*number*of*homogeneous*models**of*a com- plete*theory*[MR 90f:03066] (187-204); T. G. Mustafin,*The*stability*theory**of*polygons [MR 90b:03047] (205-223); E. A. Palyutin and S. S. ...##
###
Page 5250 of Mathematical Reviews Vol. , Issue 99h
[page]

1999
*
Mathematical Reviews
*

Let GL,,(F) be

*the**group**of*all nonsingular n x n matrices over F and U,,*the*subgroup*of*upper*unitriangular*matrices in GL,,(F). ...*The*proof uses in an essential way*the*interplay between*model**theory**of*difference fields and Diophantine geometry, as developed by E. Hrushovski. ...##
###
Page 6518 of Mathematical Reviews Vol. , Issue 93m
[page]

1993
*
Mathematical Reviews
*

*The*Mal’tsev correspondence is

*the*functor R++ UT3(R) which associates with each ring R

*the*nil-2

*group*UT3(R)

*of*all upper

*unitriangular*3 x 3 matrices over R. ... In

*the*present paper

*the*author investigates

*the*following main problem: To what extent do

*the*isomorphism type

*of*

*the*mere

*group*UT3(R) and

*the*first-order

*theory*

*of*UT3(R) determine either R or

*the*first ...

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