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A linear group is not amenable if and only if it contains a non-abelian free group (thus the von Neumann conjecture, while not true in general, holds for linear groups). The Tits alternative is an important ingredient [2] in the proof of Gromov's theorem on groups of polynomial growth. In fact the alternative essentially establishes the result ...
These are the list of federal constituencies (Bahagian Pilihan Raya Persekutuan) followed by the state constituencies (Bahagian Pilihan Raya Negeri) in Malaysia.. Each federal constituency contains 2 to 6 state constituencies, except in the Federal Territories where there are only federal constituencies.
Iskandar Puteri (formerly known as Nusajaya) is a city and the administrative capital of the state of Johor, Malaysia.It is situated along the Straits of Johor at the southern end of the Malay Peninsula, it is also the southernmost city of continental Eurasia.
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
For arbitrary groups, it is known that the hidden subgroup problem is solvable using a polynomial number of evaluations of the oracle. [3] However, the circuits that implement this may be exponential in log | G | {\displaystyle \log |G|} , making the algorithm not efficient overall; efficient algorithms must be polynomial in the number of ...
A group G is said to be linear if there exists a field K, an integer d and an injective homomorphism from G to the general linear group GL d (K) (a faithful linear representation of dimension d over K): if needed one can mention the field and dimension by saying that G is linear of degree d over K.
The quotient group is the symmetric group, and this construction is in fact the Weyl group of the general linear group: the diagonal matrices are a maximal torus in the general linear group (and are their own centralizer), the generalized permutation matrices are the normalizer of this torus, and the quotient, () / = / is the Weyl group.
In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication.This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group.