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Triples in Finite Groups and a Conjecture of Guralnick and Tiep.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Triples in Finite Groups and a Conjecture of Guralnick and Tiep./
Author:	Lee, Hyereem.
Description:	1 online resource (89 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369816037

Triples in Finite Groups and a Conjecture of Guralnick and Tiep.
Lee, Hyereem.

Triples in Finite Groups and a Conjecture of Guralnick and Tiep. - 1 online resource (89 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this thesis, we will see a way to use representation theory and the theory of linear algebraic groups to characterize certain family of finite groups. In Chapter 1, we see the history of preceding work. In particular, J. G. Thompson's classification of minimal finite simple nonsolvable groups and characterization of solvable groups will be given. In Chapter 2, we will describe some background knowledge underlying this project and notation that will be widely used in this thesis.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369816037Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Triples in Finite Groups and a Conjecture of Guralnick and Tiep.
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100 1 $a Lee, Hyereem. $3 1180723
245 1 0 $a Triples in Finite Groups and a Conjecture of Guralnick and Tiep.
264 0 $c 2017
300 $a 1 online resource (89 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Adviser: Pham Huu Tiep.
502 $a Thesis (Ph.D.) $c The University of Arizona $d 2017.
504 $a Includes bibliographical references
520 $a In this thesis, we will see a way to use representation theory and the theory of linear algebraic groups to characterize certain family of finite groups. In Chapter 1, we see the history of preceding work. In particular, J. G. Thompson's classification of minimal finite simple nonsolvable groups and characterization of solvable groups will be given. In Chapter 2, we will describe some background knowledge underlying this project and notation that will be widely used in this thesis.
520 $a In Chapter 3, the main theorem originally conjectured by Guralnick and Tiep will be stated together with the base theorem which is a reduced version of main theorem to the case where we have a quasisimple group. Main theorem explains a way to characterize the finite groups with a composition factor of order divisible by two distinct primes p and q as the finite groups containing nontrivial 2-element x, p-element y, q-element z such that xyz = 1. In this thesis we more focus on the proof of showing a finite group G with a composition factor of order divisible by two distinct prime p and q contains nontrivial 2-element x, p-element y, q-element z such that xyz = 1.
520 $a In Chapter 4, we will prove a set of lemmas and proposition which will be used as key tools in the proof of the base theorem. In Chapters 5 to 7, we will establish the base theorem in the cases where a quasisimple group G has its simple quotient isomorphic to alternating groups or sporadic groups (Chapter 5), classical groups (Chapter 6), and exceptional groups (Chapter 7).
520 $a In Chapter 8, we show that any finite group G admitting nontrivial 2-element x, p- element y, q-element z such that xyz = 1 for two distinct odd primes p and q admits a composition factor of order divisible by pq. Also, we show that the question if a finite group G with a composition factor of order divisible by two distinct prime p and q contains nontrivial 2-element x , p-element y, q-element z such that xyz = 1 can be reduced to the base theorem.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Arizona. $b Mathematics. $3 1180722
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10277454 $z click for full text (PQDT)