Orders of Perfect Groups with Dihedral Involution Centralizers

Let G be a finite group that is equal to its commutator subgroup, and suppose that G contains an element of order 2 whose centralizer in G is dihedral of 2-power order. We study the cases where this centralizer is dihedral of order 8, 16, 32, 64, 128, or 256. It is true in each case that this centralizer is a Sylow 2-subgroup of G. We then use character-theoretic techniques to generate a list of possibilities for the order of G. In the process of generating this list of possible orders, we prove several results about the structure of our group under consideration. We then strengthen the original hypotheses to require G to be non-abelian simple, and we use the results proved about the structure of G to eliminate all possible orders such that there is no non-abelian simple group of that order.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

University of Akron

Year dc:date

2013

Author dc:creator

• Strayer, Michael Christopher

Contributors dc:contributor

• Riedl, Jeffrey

• Mathematics
• simple groups
• dihedral groups
• involutions
• projective special linear groups
• character theory

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761

OAI identifier oai:identifier

oai:etd.ohiolink.edu:akron1365259761