Ad
related to: hidden subgroup function examples in excel cellscodefinity.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring , discrete logarithm , graph isomorphism , and the shortest vector problem .
Subgroup growth studies these functions, their interplay, and the characterization of group theoretical properties in terms of these functions. The theory was motivated by the desire to enumerate finite groups of given order, and the analogy with Mikhail Gromov 's notion of word growth .
An important example in the theory of Lie groups arises when is taken to be (;), the group of invertible matrices with complex entries. In that case, a basic result is the following: [ 5 ] Theorem : Suppose φ : R → G L ( n ; C ) {\displaystyle \varphi :\mathbb {R} \rightarrow \mathrm {GL} (n;\mathbb {C} )} is a one-parameter group.
A subgroup of H that is invariant under all inner automorphisms is called normal; also, an invariant subgroup. ∀φ ∈ Inn(G)： φ(H) ≤ H. Since Inn(G) ⊆ Aut(G) and a characteristic subgroup is invariant under all automorphisms, every characteristic subgroup is normal. However, not every normal subgroup is characteristic.
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a ...
Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable. For example: smoking status defining two subgroups: smokers and non-smokers.
The subgroup method is an algorithm used in the mathematical field of group theory. It is used to find the word of an element. It doesn't always return the minimal word, but it can return optimal words based on the series of subgroups that is used.
For example, consider the infinite cyclic group ℤ = b , embedded as a normal subgroup of the Baumslag–Solitar group BS(1, 2) = a, b . With respect to the chosen generating sets, the element b 2 n = a n b a − n {\displaystyle b^{2^{n}}=a^{n}ba^{-n}} is distance 2 n from the origin in ℤ , but distance 2 n + 1 from the origin in BS(1, 2) .
Ad
related to: hidden subgroup function examples in excel cellscodefinity.com has been visited by 10K+ users in the past month