Asymptotic enumeration of matrix groups
Date
2018
Authors
Tyburski, Brady A., author
Wilson, James B., advisor
Adams, Henry, committee member
Pries, Rachel, committee member
Wilson, Jesse W., committee member
Journal Title
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Volume Title
Abstract
We prove that the general linear group GLd(pe) has between pd4e/64-O(d2) and pd4e2·log2p distinct isomorphism types of subgroups. The upper bound is obtained by elementary counting methods, where as the lower bound is found by counting the number of isomorphism types of subgroups of the generalized Heisenberg group. To count these subgroups, we use nuclei of a bilinear map alongside versor products - a division analog of the tensor product.
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Subject
bilinear map
Heisenberg group
versor
general linear group
algebra
isotopism