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Minimally Simple Groups and Burnside's Theorem

Maurer, Kendall Nicole

Abstract Details

2010, Master of Science, University of Akron, Mathematics.
William Burnside’s paqb theorem is a very important result in group theory, which states that any group G of order paqb is solvable. An interesting fact about this theorem is that it was originally proven using techniques from character theory, another branch of algebra. In fact, it was about seventy years before a group-theoretic proof of Burnside’s theorem was developed through the work of Goldschmidt, Matsuyama,Bender, and other mathematicians. Their approach to proving the theorem was to show that, in essence, minimally simple groups of size paqb do not exist. Our purpose here is to use various techniques from the group-theoretic proof of Burnside’s theorem to establish and prove similar results about minimally simple groups G of arbitrary order.
James Cossey, Dr. (Advisor)
Jeffrey Riedl, PhD (Committee Member)
Antonio Quesada, PhD (Committee Member)
40 p.

Recommended Citations

Citations

  • Maurer, K. N. (2010). Minimally Simple Groups and Burnside's Theorem [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194

    APA Style (7th edition)

  • Maurer, Kendall. Minimally Simple Groups and Burnside's Theorem. 2010. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194.

    MLA Style (8th edition)

  • Maurer, Kendall. "Minimally Simple Groups and Burnside's Theorem." Master's thesis, University of Akron, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194

    Chicago Manual of Style (17th edition)