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Classifying Triply-Invariant Subspaces

Adams, Lynn I.
http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121

Abstract Details

2007, Master of Science, University of Akron, Mathematics.
Let p be a prime number and consider the vector space consisting of all p-by-p-by-pmatrices with entries taken from the field with p elements. We wish to construct, list, and describe all those subspaces that are simultaneously invariant under three particular linear transformations on this vector space. Even for small primes p, this is an extensive and difficult computational problem. Using an elaborate overall strategy based on concepts from linear algebra, we completely solve this problem for the prime p=2, and we have completed several cases of this problem for the prime p=3. This problem has connections with classification problems for certain subgroups of wreath product finite groups of prime-power order.
Jeffrey Riedl (Advisor)
186 p.
Mathematics
wreath product; linear transformations; invariant subspaces; finite group theory; three-dimensional matrices; finite vector spaces; finite fields

Recommended Citations

Citations

  • Adams, L. I. (2007). Classifying Triply-Invariant Subspaces [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121

    APA Style (7th edition)

  • Adams, Lynn. Classifying Triply-Invariant Subspaces. 2007. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121.

    MLA Style (8th edition)

  • Adams, Lynn. "Classifying Triply-Invariant Subspaces." Master's thesis, University of Akron, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121

    Chicago Manual of Style (17th edition)

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© 2007, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.