منابع مشابه
On asymptotic dimension of groups
We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdimA ∗C B <∞. B) Suppose that G′ is an HNN extension of a g...
متن کاملOn dimension growth of groups
The (asymptotic) dimension growth functions of groups were introduced by Gromov in 1999. In this paper, we show connections between dimension growth and expansion properties of graphs, Ramsey theory and the Kolmogorov-Ostrand dimension of groups and prove that all solvable subgroups of the R.Thompson group F have polynomial dimension growth. We introduce controlled dimension growth function and...
متن کاملFinite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
متن کاملMore on sequences in groups
We bring to conclusion the investigation of three problems about sequencings for finite groups: the existence of harmonious sequences in dicyclic groups, the R-sequenceability of dicyc1ic groups, and the Rsequenceability of the nonabelian groups of order pq, where p and q are primes.
متن کاملLower Bounds on Generic Algorithms in Groups
In this paper we consider generic algorithms for computational problems in cyclic groups. The model of a generic algorithm was proposed by Shoup at Eurocrypt '97. A generic algorithm is a general-purpose algorithm that does not make use of any particular property of the representation of the group elements. Shoup proved the hardness of the discrete logarithm problem and the Diie-Hellman problem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2015
ISSN: 0029-4527
DOI: 10.1215/00294527-3153570