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StrayerThesis.pdf (360.71 KB)
ETD Abstract Container
Abstract Header
Orders of Perfect Groups with Dihedral Involution Centralizers
Author Info
Strayer, Michael Christopher
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761
Abstract Details
Year and Degree
2013, Master of Science, University of Akron, Mathematics.
Abstract
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.
Committee
Jeffrey Riedl, Dr. (Advisor)
James Cossey, Dr. (Committee Member)
Hung Nguyen, Dr. (Committee Member)
Pages
76 p.
Subject Headings
Mathematics
Keywords
simple groups
;
dihedral groups
;
involutions
;
projective special linear groups
;
character theory
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Citations
Strayer, M. C. (2013).
Orders of Perfect Groups with Dihedral Involution Centralizers
[Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761
APA Style (7th edition)
Strayer, Michael.
Orders of Perfect Groups with Dihedral Involution Centralizers.
2013. University of Akron, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761.
MLA Style (8th edition)
Strayer, Michael. "Orders of Perfect Groups with Dihedral Involution Centralizers." Master's thesis, University of Akron, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761
Chicago Manual of Style (17th edition)
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Document number:
akron1365259761
Download Count:
409
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.