1,111 research outputs found
Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
In this paper we show that certain special cases of the hidden subgroup
problem can be solved in polynomial time by a quantum algorithm. These special
cases involve finding hidden normal subgroups of solvable groups and
permutation groups, finding hidden subgroups of groups with small commutator
subgroup and of groups admitting an elementary Abelian normal 2-subgroup of
small index or with cyclic factor group.Comment: 10 page
Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups and Binary Polyhedral Groups
In this article we calculate the minimal faithful permutation degree for all
of the irreducible Coxeter groups. We also exhibit new examples of finite
groups that possess a quotient whose minimal degree is strictly greater than
that of the group.Comment: 22 page
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