Finding conjugate stabilizer subgroups of almost 3-transitive groups Export

@article{citeulike:3270865, abstract = {We reduce a case of the hidden subgroup problem (HSP) in several families of finite groups of Lie type, such as SL\_2(F\_q), PSL\_2(F\_q), and PGL\_2(F\_q), to efficiently solvable HSPs in the affine group AGL\_1(F\_q). These groups act on projective space in an "almost" 3-transitive way, and we use this fact in each group to distinguish conjugates of its Borel (upper triangular) subgroup. Our observation is purely group-theoretic, and as such does not break new ground in quantum algorithms. Nonetheless, these appear to be the first positive results on the HSP in finite simple groups such as PSL\_2(F\_q).}, archivePrefix = {arXiv}, author = {Denney, Aaron and Moore, Cristopher and Russell, Alexander}, citeulike-article-id = {3270865}, citeulike-linkout-0 = {http://arxiv.org/abs/0809.2445}, citeulike-linkout-1 = {http://arxiv.org/pdf/0809.2445}, day = {15}, eprint = {0809.2445}, keywords = {hidden\_subgroup\_problem, quantum\_algorithms}, month = {Sep}, posted-at = {2008-09-16 01:42:08}, priority = {2}, title = {Finding conjugate stabilizer subgroups of almost 3-transitive groups}, url = {http://arxiv.org/abs/0809.2445}, year = {2008} }

TY - JOUR ID - citeulike:3270865 L3 - citeulike-article-id:3270865 N2 - We reduce a case of the hidden subgroup problem (HSP) in several families of finite groups of Lie type, such as SL_2(F_q), PSL_2(F_q), and PGL_2(F_q), to efficiently solvable HSPs in the affine group AGL_1(F_q). These groups act on projective space in an "almost" 3-transitive way, and we use this fact in each group to distinguish conjugates of its Borel (upper triangular) subgroup. Our observation is purely group-theoretic, and as such does not break new ground in quantum algorithms. Nonetheless, these appear to be the first positive results on the HSP in finite simple groups such as PSL_2(F_q). TI - Finding conjugate stabilizer subgroups of almost 3-transitive groups KW - hidden_subgroup_problem KW - quantum_algorithms AU - Denney, Aaron AU - Moore, Cristopher AU - Russell, Alexander PY - 2008/Sep/15/ UR - http://arxiv.org/abs/0809.2445 ER -