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A characterization of the 2-fusion system of L_4(q)
Lynd, Justin

2012, Doctor of Philosophy, Ohio State University, Mathematics.
We study saturated fusion systems F on a finite 2-group S with an involution centralizer having a unique component on a dihedral group and containing the Baumann subgroup of S. Assuming F is perfect with no nontrivial normal 2-subgroups and the centralizer of the component is a cyclic 2-group, it is shown F is uniquely determined as the 2-fusion system of L_4(q) for some q = 3 (mod 4). This should be viewed as a contribution to a program recently outlined by Aschbacher for the classification of simple fusion systems at the prime 2. The analogous problem in the classification of finite simple groups of component type (the L_2(q), A_7 standard component problem) was one of the last to be completed, and was ultimately only resolved in an inductive context with heavy machinery. Thanks primarily to the hypothesis concerning the Baumann subgroup and the absence of cores, our arguments by contrast require only 2-fusion analysis and transfer. We prove a generalization of the Thompson transfer lemma in the context of fusion systems, which is applied often.
Ronald Solomon (Advisor)
Matthew Kahle (Committee Member)
Jean-Francois Lafont (Committee Member)
Richard Lyons (Committee Member)
101 p.

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Lynd, J. (2012). A characterization of the 2-fusion system of L_4(q). (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Lynd, Justin. "A characterization of the 2-fusion system of L_4(q)." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Lynd, Justin "A characterization of the 2-fusion system of L_4(q)." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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