Classification of non abelian simple groups up to order a thousand

Postgraduate Thesis uoadl:1320344 563 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2014-01-08
Year:
2014
Author:
Λελίδης Γεώργιος
Supervisors info:
Δεριζιώτης Δημήτριος Καθηγητής ΕΚΠΑ, Εμμανουήλ Ιωάννης Καθηγητής ΕΚΠΑ, Μαλιάκας Μιχαήλ Καθηγητής ΕΚΠΑ
Original Title:
Ταξινόμηση μη αβελιανών πεπερασμένων απλών ομάδων με τάξη μικρότερη του χίλια
Languages:
Greek
Translated title:
Classification of non abelian simple groups up to order a thousand
Summary:
Α group is simple if its only normal subgroups are the trivial subgroup and the
group itself. The Abelian simple groups are the group of order one and the
cyclic groups of prime order, while the nonabelian simple groups generally have
very complicated structure.
In finite groups theory the simple groups play an important role, because via
Jordan – Hoelder theorem they can be thought as “buildings blocks” for the
finite groups. As well many questions about finite groups can be reduced to
questions about simple groups.
The primary goal of this paper is to prove and apply Sylow theorems and the
Burnside transfer theorem to the study of simple groups up to order a thousand
. More specifically, we may use the results of Sylow theorems and the Burnside
transfer theorem to determine whether or not certain positive integer numbers
up to a thousand occur αs orders of simple groups. In additional we prove that
the simple groups of order less than a thousand are unique up to isomorphism.
Keywords:
Group, Simple, Order, Transfer, Sylow
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
10
Number of pages:
80
File:
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