Search results
Results from the WOW.Com Content Network
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 ...
A normal subgroup of a normal subgroup of a group need not be normal in the group. That is, normality is not a transitive relation. The smallest group exhibiting this phenomenon is the dihedral group of order 8. [15] However, a characteristic subgroup of a normal subgroup is normal. [16] A group in which normality is transitive is called a T ...
It is not hard to give infinitely generated examples of non-linear groups: for example the infinite abelian group (Z/2Z) N x (Z/3Z) N cannot be linear. [9] Since the symmetric group on an infinite set contains this group it is also not linear. Finding finitely generated examples is subtler and usually requires the use of one of the properties ...
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.
Note that a "complex Lie group" is defined as a complex analytic manifold that is also a group whose multiplication and inversion are each given by a holomorphic map. The dimensions in the table below are dimensions over C. Note that every complex Lie group/algebra can also be viewed as a real Lie group/algebra of twice the dimension.
It was then followed by the signing of MoU by Indonesian Armed Forces and Taman Siswa, which is among the first local and formal educational groups in Indonesia, to set up and support a foundation called Lembaga Perguruan Taman Taruna Nusantara (LPTTN). It is this foundation that eventually crystallised Gen. Moerdani's vision and subsequently ...
The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons.. Shor's algorithm for factoring and for finding discrete logarithms (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite abelian groups.
More generally, a quasisimple group (a perfect central extension of a simple group) that is a non-trivial extension (and therefore not a simple group itself) is perfect but not simple; this includes all the insoluble non-simple finite special linear groups SL(n,q) as extensions of the projective special linear group PSL(n,q) (SL(2,5) is an ...