Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOD-Characterization of Some Simple Unitary Groups
190
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The degree pattern of a finite group is the degree sequence of its prime graph in ascending order of vertices. We say that the problem of OD-characterization is solved for a finite group if we determine the number of pairwise nonisomorphic finite groups with the same order and degree pattern as the group under consideration. In this article the problem of OD-characterization is solved for some simple unitary groups. It was shown, in particular, that the simple unitary groups $U_3(q)$ and $U_4(q)$ are OD-characterizable, where $q$ is a prime power $<10^2$.
rate research
Read More
It is proved that finite nonabelian simple groups $S$ with $max pi(S)=37$ are uniquely determined by their order and degree pattern in the class of all finite groups.
We provide the first examples of words in the free group of rank 2 which are not proper powers and for which the corresponding word maps are non-surjective on an infinite family of finite non-abelian simple groups.
This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a special attention is paid to the case of discrete groups. The unitary dual of a group $G$ is the space of equivalence classes of its irreducible unitary representations; it is both a topological space and a Borel space. The primitive dual is the space of weak equivalence classes of unitary irreducible representations. The normal quasi-dual is the space of quasi-equivalence classes of traceable factor representations; it is parametrized by characters, which can be finite or infinite. The theory is systematically illustrated by a series of specific examples: Heisenberg groups, affine groups of infinite fields, solvable Baumslag-Solitar groups, lamplighter groups, and general linear groups. Operator algebras play an important role in the exposition, in particular the von Neumann algebras associated to a unitary representation and C*-algebras associated to a locally compact group.
We generalize a result of R. Thomas to establish the non-vanishing of the first l2-Betti number for a class of finitely generated groups.
We show that the group of almost automorphisms of a d-regular tree does not admit lattices. As far as we know this is the first such example among (compactly generated) simple locally compact groups.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
