Tyburski, Brady A., authorWilson, James B., advisorAdams, Henry, committee memberPries, Rachel, committee memberWilson, Jesse W., committee member2018-09-102018-09-102018https://hdl.handle.net/10217/191288We 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.born digitalmasters thesesengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.bilinear mapHeisenberg groupversorgeneral linear groupalgebraisotopismText