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

Lynd, Justin
http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920

Abstract Details

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.
Mathematics
fusion system; p-local finite group; classification of finite simple groups

Recommended Citations

Citations

  • Lynd, J. (2012). A characterization of the 2-fusion system of L_4(q) [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920

    APA Style (7th edition)

  • Lynd, Justin. A characterization of the 2-fusion system of L_4(q). 2012. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920.

    MLA Style (8th edition)

  • Lynd, Justin. "A characterization of the 2-fusion system of L_4(q)." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920

    Chicago Manual of Style (17th edition)

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© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.