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On some Density Theorems in Number T...

Bardestani, Mohammad.

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On some Density Theorems in Number Theory and Group Theory.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On some Density Theorems in Number Theory and Group Theory./
Author:	Bardestani, Mohammad.
Description:	140 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
Contained By:	Dissertation Abstracts International74-07B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR79273
ISBN:	9780494792735

On some Density Theorems in Number Theory and Group Theory.
Bardestani, Mohammad.

On some Density Theorems in Number Theory and Group Theory. - 140 p.

Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.

Thesis (Ph.D.)--Universite de Montreal (Canada), 2013.

Gowers [31] in his paper on quasirandom groups studies a question of Babai and Sos asking whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|. Answering the question negatively, he proves that for sufficiently large prime p, the group PSL2( Fp ) has no product-free subset of size ≥ cn 8/9, where n is the order of PSL2( Fp ).

ISBN: 9780494792735Subjects--Topical Terms:

515831
Mathematics.

On some Density Theorems in Number Theory and Group Theory.
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020 $a 9780494792735
035 $a (MiAaPQ)AAINR79273
035 $a AAINR79273
040 $a MiAaPQ $c MiAaPQ
100 1 $a Bardestani, Mohammad. $3 2105013
245 1 0 $a On some Density Theorems in Number Theory and Group Theory.
300 $a 140 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
500 $a Adviser: Andrew Granville.
502 $a Thesis (Ph.D.)--Universite de Montreal (Canada), 2013.
520 $a Gowers [31] in his paper on quasirandom groups studies a question of Babai and Sos asking whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|. Answering the question negatively, he proves that for sufficiently large prime p, the group PSL2( Fp ) has no product-free subset of size ≥ cn 8/9, where n is the order of PSL2( Fp ).
520 $a We will consider the problem for compact groups and in particular for the profinite groups SLk( Zp ) and Sp2k( Zp ). In Part I of this thesis, we obtain lower and upper exponential bounds for the supremal measure of the product-free sets. The proof involves establishing a lower bound for the dimension of non-trivial representations of the finite groups SLk( Z /(pn Z )) and Sp2k( Z /(pn Z )). Indeed, our theorem extends and simplifies previous work of Landazuri and Seitz [49], where they consider the minimal degree of representations for Chevalley groups over a finite field.
520 $a In Part II of this thesis, we move to algebraic number theory. A monogenic polynomial f is a monic irreducible polynomial with integer coefficients which produces a monogenic number field. For a given prime q, using the Chebotarev density theorem, we will show the density of primes p, such that tq -- p is monogenic, is greater than or equal to (q -- 1)/q. We will also prove that, when q = 3, the density of primes p, which Q&parl0;p3&parr0; is non-monogenic, is at least 1/9.
520 $a Keywords. Profinite group, Complex representation, Hilbert-Schmidt operator, Singular value decomposition, Chebotarev density theorem, Monogenic field, Thue equation..
590 $a School code: 0992.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0405
690 $a 0642
710 2 $a Universite de Montreal (Canada). $b Faculte des arts et des sciences. $3 2092553
773 0 $t Dissertation Abstracts International $g 74-07B(E).
790 $a 0992
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR79273