Constructions and simplicity of the Mathieu groups
Author(s)
Advisor
Gelvin, Matthew Justin KarcherDate
2020-08Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Of the 26 sporadic finite simple groups, 5 were discovered by E. Mathieu in 1861
and 1873 [1], [2]. These Mathieu groups are the focus of this thesis, where we will
prove their simplicity using elementary methods. E. Witt [5] realized a connection
between the Mathieu groups and certain combinatorial structures known as Steiner
systems. We will follow his construction to define the Mathieu groups as the automorphism groups of certain Steiner systems. Much of the work of the thesis lies in the construction of these Steiner systems, which we achieve by using both methods
from finite geometry and the theory of Golay codes.